51
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Boettcher S, Robe DM, Sibani P. Aging is a log-Poisson process, not a renewal process. Phys Rev E 2018; 98:020602. [PMID: 30253586 DOI: 10.1103/physreve.98.020602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Indexed: 06/08/2023]
Abstract
Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a nonequilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process such as CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations ("quakes"). We show that such a record dynamics provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.
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Affiliation(s)
- Stefan Boettcher
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Dominic M Robe
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Paolo Sibani
- Institut for Fysik Kemi og Farmaci, Syddansk Universitet, DK-5230 Odense M, Denmark
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52
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Seoane B, Zamponi F. Spin-glass-like aging in colloidal and granular glasses. SOFT MATTER 2018; 14:5222-5234. [PMID: 29892754 DOI: 10.1039/c8sm00859k] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure PG separates two distinct dynamical regimes. For pressure P < PG, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrate within the glass free energy basin. For P > PG, instead, the dynamics become strongly anomalous, displaying very large equilibration timescales, aging, and a constantly increasing dynamical susceptibility. The crossover at PG is strongly reminiscent of the one observed in three-dimensional spin-glasses in an external field, suggesting that the two systems could be in the same universality class, consistent with theoretical expectations.
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Affiliation(s)
- Beatriz Seoane
- Laboratoire de physique théorique, Département de physique de l'ENS, École normale supérieure, PSL Research University, Sorbonne Universités, CNRS, 75005 Paris, France
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53
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Crisanti A, Picco M, Ritort F. Derivation of the spin-glass order parameter from stochastic thermodynamics. Phys Rev E 2018; 97:052103. [PMID: 29906861 DOI: 10.1103/physreve.97.052103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Indexed: 06/08/2023]
Abstract
A fluctuation relation is derived to extract the order parameter function q(x) in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap q between configurations. For a fixed value of q, entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the q(x) in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.
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Affiliation(s)
- A Crisanti
- Dipartimento di Fisica, Università di Roma "La Sapienza", and Istituto dei Sistemi Complessi ISC-CNR, P.le Aldo Moro 2, 00185 Roma, Italy
| | - M Picco
- Sorbonne Université, CNRS, Université Pierre et Marie Curie, LPTHE, F-75005 Paris, France
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Martí i Franquès, E-08028, Barcelona, Spain
- CIBER-BBN Center for Bioengineering, Biomaterials and Nanomedicine, Instituto de Salud Carlos III, Madrid, Spain
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54
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55
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Niss K. Mapping Isobaric Aging onto the Equilibrium Phase Diagram. PHYSICAL REVIEW LETTERS 2017; 119:115703. [PMID: 28949204 DOI: 10.1103/physrevlett.119.115703] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2017] [Indexed: 06/07/2023]
Abstract
The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts of phase space that are not accessed by the equilibrium liquid. It is found that the temperature dependence of relaxation time is non-Arrhenius even in the isostructural case-challenging the Adam-Gibbs entropy model. Based on the presented data and the idea that aging happens through quasiequilibrium states, we suggest a mapping of the out-of-equilibrium states during isobaric aging to the equilibrium phase diagram. This mapping implies the existence of isostructural lines in the equilibrium phase diagram. The relaxation time is found to depend on the bath temperature, density, and a just single structural parameter, referred to as an effective temperature.
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Affiliation(s)
- Kristine Niss
- Glass & Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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56
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Jin Y, Yoshino H. Exploring the complex free-energy landscape of the simplest glass by rheology. Nat Commun 2017; 8:14935. [PMID: 28397805 PMCID: PMC5394243 DOI: 10.1038/ncomms14935] [Citation(s) in RCA: 53] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2016] [Accepted: 02/08/2017] [Indexed: 11/09/2022] Open
Abstract
For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of amorphous solids revealed the possibility of unexpectedly complex free-energy landscapes where the simple harmonic picture breaks down. Here we demonstrate that standard rheological techniques can be used as powerful tools to examine nontrivial consequences of such complex free-energy landscapes. By extensive numerical simulations on a hard sphere glass under quasistatic shear at finite temperatures, we show that above the so-called Gardner transition density, the elasticity breaks down, the stress relaxation exhibits slow, and ageing dynamics and the apparent shear modulus becomes protocol-dependent. Being designed to be reproducible in laboratories, our approach may trigger explorations of the complex free-energy landscapes of a large variety of amorphous materials.
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Affiliation(s)
- Yuliang Jin
- Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Hajime Yoshino
- Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
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57
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Lahini Y, Gottesman O, Amir A, Rubinstein SM. Nonmonotonic Aging and Memory Retention in Disordered Mechanical Systems. PHYSICAL REVIEW LETTERS 2017; 118:085501. [PMID: 28282188 DOI: 10.1103/physrevlett.118.085501] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2016] [Indexed: 05/22/2023]
Abstract
We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.
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Affiliation(s)
- Yoav Lahini
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Omer Gottesman
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ariel Amir
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Shmuel M Rubinstein
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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58
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Baity-Jesi M, Calore E, Cruz A, Fernandez LA, Gil-Narvión JM, Gordillo-Guerrero A, Iñiguez D, Maiorano A, Marinari E, Martin-Mayor V, Monforte-Garcia J, Muñoz Sudupe A, Navarro D, Parisi G, Perez-Gaviro S, Ricci-Tersenghi F, Ruiz-Lorenzo JJ, Schifano SF, Seoane B, Tarancón A, Tripiccione R, Yllanes D. A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements. Proc Natl Acad Sci U S A 2017; 114:1838-1843. [PMID: 28174274 PMCID: PMC5338409 DOI: 10.1073/pnas.1621242114] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We have performed a very accurate computation of the nonequilibrium fluctuation-dissipation ratio for the 3D Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.
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Affiliation(s)
- Marco Baity-Jesi
- Institut de Physique Théorique, Direction de la Recherche Fondamentale, Commissariat à L'énergie Atomique et aux Énergies Alternatives, Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Enrico Calore
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara e Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Ferrara, I-44122 Ferrara, Italy
| | - Andres Cruz
- Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
| | - Luis Antonio Fernandez
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | | | - Antonio Gordillo-Guerrero
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Ingeniería Eléctrica, Electrónica y Automática, Universidad de Extremadura, 10071, Cáceres, Spain
| | - David Iñiguez
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Fundación Agencia Aragonesa para la Investigación y Desarrollo, Diputación General de Aragón, 50003 Zaragoza, Spain
| | - Andrea Maiorano
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
- Nanotec-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
| | - Victor Martin-Mayor
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | | | - Antonio Muñoz Sudupe
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | - Denis Navarro
- Departamento de Ingeniería, Electrónica y Comunicaciones and I3A, Universidad de Zaragoza, 50018 Zaragoza, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy;
- Nanotec-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
| | - Sergio Perez-Gaviro
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Centro Universitario de la Defensa, 50090 Zaragoza, Spain
| | - Federico Ricci-Tersenghi
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
- Nanotec-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
| | - Juan Jesus Ruiz-Lorenzo
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Institut de Physique Théorique, Direction de la Recherche Fondamentale, Commissariat à L'énergie Atomique et aux Énergies Alternatives, Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Sebastiano Fabio Schifano
- Dipartimento di Matematica e Informatica, Università di Ferrara e INFN, Sezione di Ferrara, I-44122 Ferrara, Italy
| | - Beatriz Seoane
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain;
- Laboratoire de Physique Théorique, École Normale Supérieure, Université de Recherche Paris Sciences et Lettres, Pierre et Marie Curie, Sorbonne Universités, UMR 8549 CNRS, 75005 Paris, France
| | - Alfonso Tarancón
- Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
| | - Raffaele Tripiccione
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara e Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Ferrara, I-44122 Ferrara, Italy
| | - David Yllanes
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Department of Physics and Soft Matter Program, Syracuse University, Syracuse, NY 13244
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59
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Ric A, Torrents C, Gonçalves B, Sampaio J, Hristovski R. Soft-assembled Multilevel Dynamics of Tactical Behaviors in Soccer. Front Psychol 2016; 7:1513. [PMID: 27761120 PMCID: PMC5050225 DOI: 10.3389/fpsyg.2016.01513] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2016] [Accepted: 09/20/2016] [Indexed: 02/04/2023] Open
Abstract
This study aimed to identify the tactical patterns and the timescales of variables during a soccer match, allowing understanding the multilevel organization of tactical behaviors, and to determine the similarity of patterns performed by different groups of teammates during the first and second halves. Positional data from 20 professional male soccer players from the same team were collected using high frequency global positioning systems (5 Hz). Twenty-nine categories of tactical behaviors were determined from eight positioning-derived variables creating multivariate binary (Boolean) time-series matrices. Hierarchical principal component analysis (PCA) was used to identify the multilevel structure of tactical behaviors. The sequential reduction of each set level of principal components revealed a sole principal component as the slowest collective variable, forming the global basin of attraction of tactical patterns during each half of the match. In addition, the mean dwell time of each positioning-derived variable helped to understand the multilevel organization of collective tactical behavior during a soccer match. This approach warrants further investigations to analyze the influence of task constraints on the emergence of tactical behavior. Furthermore, PCA can help coaches to design representative training tasks according to those tactical patterns captured during match competitions and to compare them depending on situational variables.
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Affiliation(s)
- Angel Ric
- Complex Systems in Sport Research Group, National Institute of Physical Education of Catalonia, University of Lleida Lleida, Spain
| | - Carlota Torrents
- Complex Systems in Sport Research Group, National Institute of Physical Education of Catalonia, University of Lleida Lleida, Spain
| | - Bruno Gonçalves
- CreativeLab Research Community, Research Centre in Sports Sciences, Health Sciences and Human Development, CIDESD, Universidade de Trás-os-Montes e Alto Douro Vila Real, Portugal
| | - Jaime Sampaio
- CreativeLab Research Community, Research Centre in Sports Sciences, Health Sciences and Human Development, CIDESD, Universidade de Trás-os-Montes e Alto Douro Vila Real, Portugal
| | - Robert Hristovski
- Faculty of Physical Education, Sport and Health, Saints Cyril and Methodius University Skopje, Macedonia
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60
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Cortés-Morales EC, Elizondo-Aguilera LF, Medina-Noyola M. Equilibration and Aging of Liquids of Non-Spherically Interacting Particles. J Phys Chem B 2016; 120:7975-87. [DOI: 10.1021/acs.jpcb.6b04635] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ernesto C. Cortés-Morales
- Instituto
de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí,
SLP, México
| | - L. F. Elizondo-Aguilera
- Departamento
de Ingeniería Física, División de Ciencias e
Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, México
- Institut für
Materialphysik im Weltraum, Deutsches Zentrum für Luft-und
Raumfahrt (DLR), 51170 Köln, Germany
| | - M. Medina-Noyola
- Instituto
de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí,
SLP, México
- Departamento
de Ingeniería Física, División de Ciencias e
Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, México
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61
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Nandi SK, Ramaswamy S. Glass susceptibility: Growth kinetics and saturation under shear. Phys Rev E 2016; 94:012607. [PMID: 27575179 DOI: 10.1103/physreve.94.012607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2016] [Indexed: 06/06/2023]
Abstract
We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function χ_{C}(t,t_{w}) with time t and waiting time t_{w}. From the complete wave-vector-dependent equations of motion for domain growth, we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value χ_{C}^{P} of χ_{C}(t,t_{w}), which can be viewed as a correlation volume, grows as t_{w}^{0.5}, and the relaxation time as t_{w}^{0.8}, following a quench to a point deep in the glassy state. These results constitute a theoretical explanation of the simulation findings of Parisi [J. Phys. Chem. B 103, 4128 (1999)JPCBFK1520-610610.1021/jp983967m] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)PRLTAO0031-900710.1103/PhysRevLett.78.4581], and they are also in qualitative agreement with Parsaeian and Castillo [Phys. Rev. E 78, 060105(R) (2008)PLEEE81539-375510.1103/PhysRevE.78.060105]. On the other hand, if the quench is to a point on the liquid side, the correlation volume grows to saturation. We present a similar calculation for the growth kinetics in a p-spin spin glass mean-field model where we find a slower growth, χ_{C}^{P}∼t_{w}^{0.13}. Further, we show that a shear rate γ[over ̇] cuts off the growth of glassy correlations when t_{w}∼1/γ[over ̇] for quench in the glassy regime and t_{w}=min(t_{r},1/γ[over ̇]) in the liquid, where t_{r} is the relaxation time of the unsheared liquid. The relaxation time of the steady-state fluid in this case is ∝γ[over ̇]^{-0.8}.
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Affiliation(s)
- Saroj Kumar Nandi
- Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore 560 012, India
| | - Sriram Ramaswamy
- Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore 560 012, India
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
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62
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Corberi F, Villavicencio-Sanchez R. Role of initial state and final quench temperature on aging properties in phase-ordering kinetics. Phys Rev E 2016; 93:052105. [PMID: 27300828 DOI: 10.1103/physreve.93.052105] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Indexed: 11/07/2022]
Abstract
We study numerically the two-dimensional Ising model with nonconserved dynamics quenched from an initial equilibrium state at the temperature T_{i}≥T_{c} to a final temperature T_{f} below the critical one. By considering processes initiating both from a disordered state at infinite temperature T_{i}=∞ and from the critical configurations at T_{i}=T_{c} and spanning the range of final temperatures T_{f}∈[0,T_{c}[ we elucidate the role played by T_{i} and T_{f} on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T_{f}, while the autocorrelation function exponent λ_{C} takes a markedly different value for T_{i}=∞ [λ_{C}(T_{i}=∞)≃5/4] or T_{i}=T_{c} [λ_{C}(T_{i}=T_{c})≃1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T_{f} is considered, although this is expected to play no role in the large-scale and long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T_{f}=0 are consistent with a value of the response function exponent λ_{χ}=1/2λ_{C}(T_{i}=∞)=5/8 different from the one [λ_{χ}∈(0.5-0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important preasymptotic corrections associated to T_{f}>0.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Rodrigo Villavicencio-Sanchez
- Dipartimento di Fisica "E. R. Caianiello", Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
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63
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Micoulaut M. Relaxation and physical aging in network glasses: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:066504. [PMID: 27213928 DOI: 10.1088/0034-4885/79/6/066504] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.
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Affiliation(s)
- Matthieu Micoulaut
- Paris Sorbonne Universités, LPTMC-UPMC, 4 place Jussieu, 75252 Paris cedex 05, France
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64
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de Candia A, Fierro A, Coniglio A. Scaling and universality in glass transition. Sci Rep 2016; 6:26481. [PMID: 27221056 PMCID: PMC4879566 DOI: 10.1038/srep26481] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2016] [Accepted: 04/22/2016] [Indexed: 11/12/2022] Open
Abstract
Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator 〈q(t)〉 and the dynamical susceptibility 〈q(2)(t)〉 - 〈q(t)〉(2). Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al. (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension dc = 8.
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Affiliation(s)
- Antonio de Candia
- Dipartimento di Fisica “Ettore Pancini”, Università di Napoli “Federico II”, Complesso Universitario di Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy
- CNR-SPIN, via Cintia, 80126 Napoli, Italy
- INFN, Sezione di Napoli, via Cintia, 80126 Napoli, Italy
| | - Annalisa Fierro
- Dipartimento di Fisica “Ettore Pancini”, Università di Napoli “Federico II”, Complesso Universitario di Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy
- CNR-SPIN, via Cintia, 80126 Napoli, Italy
| | - Antonio Coniglio
- Dipartimento di Fisica “Ettore Pancini”, Università di Napoli “Federico II”, Complesso Universitario di Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy
- CNR-SPIN, via Cintia, 80126 Napoli, Italy
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65
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Sullivan NS, Hamida JA, Pilla S, Muttalib KA, Genio E. Molecular glasses: NMR and dielectric susceptibility measurements. J STRUCT CHEM+ 2016. [DOI: 10.1134/s0022476616020098] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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66
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Maimbourg T, Kurchan J, Zamponi F. Solution of the Dynamics of Liquids in the Large-Dimensional Limit. PHYSICAL REVIEW LETTERS 2016; 116:015902. [PMID: 26799030 DOI: 10.1103/physrevlett.116.015902] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Indexed: 06/05/2023]
Abstract
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions d. The derivation is long but straightforward: a dynamic virial expansion for which only the first two terms survive, followed by a change to generalized spherical coordinates in the dynamic variables leading to saddle-point evaluation of integrals for large d. The problem is, thus, mapped onto a one-dimensional diffusion in a perturbed harmonic potential with colored noise. At high density, an ergodicity-breaking glass transition is found. In this regime, our results agree with thermodynamics, consistently with the general random first order transition scenario. The glass transition density is higher than the best known lower bound for hard sphere packings in large d. Because our calculation is, if not rigorous, elementary, an improvement in the bound for sphere packings in large dimensions is at hand.
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Affiliation(s)
- Thibaud Maimbourg
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, Paris 75005, France
| | - Jorge Kurchan
- LPS, École Normale Supérieure, UMR 8550 CNRS, 24 Rue Lhomond, Paris 75005, France
| | - Francesco Zamponi
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, Paris 75005, France
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67
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Martiniani S, Schrenk KJ, Stevenson JD, Wales DJ, Frenkel D. Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings. Phys Rev E 2016; 93:012906. [PMID: 26871142 DOI: 10.1103/physreve.93.012906] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2015] [Indexed: 06/05/2023]
Abstract
We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011)10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014)10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.
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Affiliation(s)
- Stefano Martiniani
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - K Julian Schrenk
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jacob D Stevenson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Microsoft Research Ltd, 21 Station Road, Cambridge CB1 2FB, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Daan Frenkel
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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68
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Rainone C, Ferrari U, Paoluzzi M, Leuzzi L. Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062150. [PMID: 26764675 DOI: 10.1103/physreve.92.062150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2015] [Indexed: 06/05/2023]
Abstract
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with p-body quenched disordered interaction, with p>2, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.
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Affiliation(s)
- Corrado Rainone
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
- LPT, Ecole Normale Supérieure, CNRS UMR 8549, 24 Rue Lhomond, 75005 Paris, France
| | - Ulisse Ferrari
- Institut de la Vision, Sorbonne Universités, UPMC, INSERM U968, CNRS UMR 7210, Paris, F-75012, France
| | - Matteo Paoluzzi
- Department of Physics, Syracuse University, Syracuse NY 13244, USA
| | - Luca Leuzzi
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
- NANOTEC-CNR, Soft and Living Matter Lab. Rome, c/o Dept. Physics, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
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69
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Olais-Govea JM, López-Flores L, Medina-Noyola M. Non-equilibrium theory of arrested spinodal decomposition. J Chem Phys 2015; 143:174505. [DOI: 10.1063/1.4935000] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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70
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Sakuldee F, Suwanna S. Linear response and modified fluctuation-dissipation relation in random potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052118. [PMID: 26651658 DOI: 10.1103/physreve.92.052118] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Indexed: 06/05/2023]
Abstract
In this work, a physical system described by the Hamiltonian H(ω)=H(0)+V(ω)(t) consisting of a solvable model H(0) and external random and time-dependent potential V(ω)(t) is investigated. Under the conditions in which, for each realization, the potential changes smoothly so that the evolution of the system follows the Schrödinger dynamics, and that the average external potential with respect to all realizations is constant in time, an adjusted equilibrium state can be defined as a reference state and the mean dynamics can be derived from taking the average of the equation with respect to the configuration parameter ω. It provides extra contributions from the deviations of the Hamiltonian and evolves the state along the time by the Heisenberg and Liouville-von Neumann equations. Consequently, the Kubo formula and the fluctuation-dissipation relation (FDR) are modified in the sense that the contribution from the information of randomness and memory effects from the time dependence is also present. The modified Kubo formula now has a contribution from two terms. The first term is an antisymmetric cross correlation between two observables measured by a probe as expected, and the latter term is an accumulation of the propagation of the effects from the randomness. When the considered system is in the adjusted equilibrium state at the time the measurement probe interacts, the latter contribution vanishes, and the standard FDR is recovered.
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Affiliation(s)
- Fattah Sakuldee
- MU-NECTEC Collaborative Research Unit on Quantum Information, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
| | - Sujin Suwanna
- MU-NECTEC Collaborative Research Unit on Quantum Information, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
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71
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Ettoumi W, Kasparian J, Wolf JP. Spin-Glass Model Governs Laser Multiple Filamentation. PHYSICAL REVIEW LETTERS 2015; 115:033902. [PMID: 26230795 DOI: 10.1103/physrevlett.115.033902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Indexed: 06/04/2023]
Abstract
We show that multiple filamentation patterns in high-power laser beams can be described by means of two statistical physics concepts, namely, self-similarity of the patterns over two nested scales and nearest-neighbor interactions of classical rotators. The resulting lattice spin model perfectly reproduces the evolution of intense laser pulses as simulated by the nonlinear Schrödinger equation, shedding new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by 2 orders of magnitude as compared to the standard simulation methods of laser filamentation.
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Affiliation(s)
- W Ettoumi
- Université de Genève, GAP-Biophotonics, Chemin de Pinchat 22, CH-1211 Geneva 4, Switzerland
| | - J Kasparian
- Université de Genève, GAP-Non-linear, Chemin de Pinchat 22, CH-1211 Geneva 4, Switzerland
| | - J-P Wolf
- Université de Genève, GAP-Biophotonics, Chemin de Pinchat 22, CH-1211 Geneva 4, Switzerland
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72
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Cammarota C, Marinari E. Spontaneous energy-barrier formation in entropy-driven glassy dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:010301. [PMID: 26274105 DOI: 10.1103/physreve.92.010301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2014] [Indexed: 06/04/2023]
Abstract
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough potential energy landscape and we analyze it both numerically and analytically. The model provides an example of dynamics where typical relaxation channels go over finite-potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space; we expect this phenomenon to be also relevant in the thermally activated regime of realistic models of glass-formers. In this case, we found that typical dynamical paths episodically reach an high-fixed-threshold energy, unexpectedly giving rise to a simple thermally activated aging phenomenology. In order to unveil this peculiar aging behavior, we introduce a novel description of the dynamics in terms of spontaneously emerging dynamical basins.
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Affiliation(s)
- Chiara Cammarota
- Sapienza, University of Rome P.le Aldo Moro 2, I-00185 Rome, Italy
| | - Enzo Marinari
- Sapienza, University of Rome and IPCF-CNR, UOS Rome P.le Aldo Moro 2, I-00185 Rome, Italy
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73
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Charbonneau P, Jin Y, Parisi G, Rainone C, Seoane B, Zamponi F. Numerical detection of the Gardner transition in a mean-field glass former. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012316. [PMID: 26274170 DOI: 10.1103/physreve.92.012316] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Indexed: 06/04/2023]
Abstract
Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.
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Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Yuliang Jin
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
| | - Corrado Rainone
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Beatriz Seoane
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Francesco Zamponi
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
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74
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75
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Elizondo-Aguilera LF, Zubieta Rico PF, Ruiz-Estrada H, Alarcón-Waess O. Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052301. [PMID: 25493790 DOI: 10.1103/physreve.90.052301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2013] [Indexed: 06/04/2023]
Abstract
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
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Affiliation(s)
- L F Elizondo-Aguilera
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, PUE, México
| | - P F Zubieta Rico
- Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | - H Ruiz-Estrada
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, PUE, México
| | - O Alarcón-Waess
- Departamento de Actuaría, Física y Matemáticas, Universidad de las Américas Puebla, Sta Catarina Mártir, C.P. 72810, Puebla, México
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76
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Sharma A, Andreanov A, Müller M. Avalanches and hysteresis in frustrated superconductors and XY spin glasses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042103. [PMID: 25375434 DOI: 10.1103/physreve.90.042103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Indexed: 06/04/2023]
Abstract
We study avalanches along the hysteresis loop of long-range interacting spin glasses with continuous XY symmetry, which serves as a toy model of granular superconductors with long-range and frustrated Josephson couplings. We identify sudden jumps in the T=0 configurations of the XY phases as an external field is increased. They are initiated by the softest mode of the inverse susceptibility matrix becoming unstable, which induces an avalanche of phase updates (or spin alignments). We analyze the statistics of these events and study the correlation between the nonlinear avalanches and the soft mode that initiates them. We find that the avalanches follow the directions of a small fraction of the softest modes of the inverse susceptibility matrix, similarly as was found in avalanches in jammed systems. In contrast to the similar Ising spin glass (Sherrington-Kirkpatrick) studied previously, we find that avalanches are not distributed with a scale-free power law but rather have a typical size which scales with the system size. We also observe that the Hessians of the spin-glass minima are not part of standard random matrix ensembles as the lowest eigenvector has a fractal support.
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Affiliation(s)
- Auditya Sharma
- International Institute of Physics, Federal University of Rio Grande do Norte, Natal, RN, Brazil and Tel Aviv University, Tel Aviv, Israel
| | - Alexei Andreanov
- The Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy and Max Planck Institute for Physics of Complex Systems Nöthnitzer Str. 38, 01187 Dresden, Germany
| | - Markus Müller
- The Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
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77
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Fractal free energy landscapes in structural glasses. Nat Commun 2014; 5:3725. [PMID: 24759041 DOI: 10.1038/ncomms4725] [Citation(s) in RCA: 217] [Impact Index Per Article: 21.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2013] [Accepted: 03/26/2014] [Indexed: 11/08/2022] Open
Abstract
Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasi-contacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here.
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78
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Béland LK, Anahory Y, Smeets D, Guihard M, Brommer P, Joly JF, Pothier JC, Lewis LJ, Mousseau N, Schiettekatte F. Replenish and relax: explaining logarithmic annealing in ion-implanted c-Si. PHYSICAL REVIEW LETTERS 2013; 111:105502. [PMID: 25166679 DOI: 10.1103/physrevlett.111.105502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Indexed: 06/03/2023]
Abstract
We study ion-damaged crystalline silicon by combining nanocalorimetric experiments with an off-lattice kinetic Monte Carlo simulation to identify the atomistic mechanisms responsible for the structural relaxation over long time scales. We relate the logarithmic relaxation, observed in a number of disordered systems, with heat-release measurements. The microscopic mechanism associated with this logarithmic relaxation can be described as a two-step replenish and relax process. As the system relaxes, it reaches deeper energy states with logarithmically growing barriers that need to be unlocked to replenish the heat-releasing events leading to lower-energy configurations.
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Affiliation(s)
- Laurent Karim Béland
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Yonathan Anahory
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Dries Smeets
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Matthieu Guihard
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Peter Brommer
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Jean-François Joly
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Jean-Christophe Pothier
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Laurent J Lewis
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - Normand Mousseau
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
| | - François Schiettekatte
- Regroupement Québécois sur les Matériaux de Pointe (RQMP), Département de physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada
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79
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Rizzo T. Replica-symmetry-breaking transitions and off-equilibrium dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032135. [PMID: 24125241 DOI: 10.1103/physreve.88.032135] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2013] [Indexed: 06/02/2023]
Abstract
I consider branches of replica-symmetry-breaking (RSB) solutions in glassy systems that display a dynamical transition at a temperature T_{d} characterized by a mode-coupling-theory dynamical behavior. Below T_{d} these branches of solutions are considered to be relevant to the system complexity and to off-equilibrium dynamics. Under general assumptions I argue that near T_{d} it is not possible to stabilize the one-step (1RSB) solution beyond the marginal point by making a full RSB (FRSB) ansatz. However, depending on the model, there may exist a temperature T strictly lower than T_{d} below which the 1RSB branch can be continued to a FRSB branch. Such a temperature certainly exists for models that display the so-called Gardner transition and in this case T_{G}<T_<T_{d}. An analytical study in the context of the truncated model reveals that the FRSB branch of solutions below T is characterized by a two-plateau structure and it ends where the first plateau disappears. These general features are confirmed in the context of the Ising p-spin model with p=3 by means of a numerical solution of the FRSB equations. The results are discussed in connection with off-equilibrium dynamics within Cugliandolo-Kurchan theory. In this context I assume that the RSB solution relevant for off-equilibrium dynamics is the 1RSB marginal solution in the whole range (T ,T_{d}) and it is the end point of the FRSB branch for T<T. Remarkably, under these assumptions it can be argued that T marks a qualitative change in off-equilibrium dynamics in the sense that the decay of various dynamical quantities changes from power law to logarithmic.
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Affiliation(s)
- Tommaso Rizzo
- IPCF-CNR, UOS Rome, and Dipartimento di Fisica, Università "Sapienza", Piazzale A. Moro 2, I-00185, Rome, Italy
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80
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Kurchan J, Parisi G, Urbani P, Zamponi F. Exact Theory of Dense Amorphous Hard Spheres in High Dimension. II. The High Density Regime and the Gardner Transition. J Phys Chem B 2013; 117:12979-94. [DOI: 10.1021/jp402235d] [Citation(s) in RCA: 112] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jorge Kurchan
- LPS, École Normale Supérieure,
UMR 8550 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Giorgio Parisi
- Dipartimento di Fisica, Universitá
di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma I, IPFC - CNR, P.le A. Moro 2, I-00185
Roma, Italy
| | - Pierfrancesco Urbani
- Dipartimento di Fisica, Universitá
di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy
- Laboratoire de
Physique Théorique et Modèles Statistiques, CNRS et
Université Paris-Sud 11, UMR8626, Bât. 100, 91405 Orsay
Cedex, France
| | - Francesco Zamponi
- LPT, École
Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
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81
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Mehta D, Stariolo DA, Kastner M. Energy landscape of the finite-size spherical three-spin glass model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052143. [PMID: 23767523 DOI: 10.1103/physreve.87.052143] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2013] [Indexed: 06/02/2023]
Abstract
We study the three-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial homotopy continuation method. On the basis of these stationary points, we analyze the complexity and other quantities related to the glass transition of the model and compare these finite-system quantities to their exact counterparts in the thermodynamic limit.
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Affiliation(s)
- Dhagash Mehta
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
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82
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Franz S, Parisi G, Ricci-Tersenghi F, Rizzo T, Urbani P. A note on weakly discontinuous dynamical transitions. J Chem Phys 2013; 138:064504. [DOI: 10.1063/1.4790517] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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83
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Gnan N, Maggi C, Parisi G, Sciortino F. Generalized fluctuation-dissipation relation and effective temperature upon heating a deeply supercooled liquid. PHYSICAL REVIEW LETTERS 2013; 110:035701. [PMID: 23373934 DOI: 10.1103/physrevlett.110.035701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2012] [Indexed: 06/01/2023]
Abstract
We show that a generalized fluctuation-dissipation relation applies upon instantaneously increasing the temperature of a deeply supercooled liquid. This has the same two-step shape of the relation found upon cooling the liquid, but with opposite violation, indicating an effective temperature that is lower than bath temperature. We show that the effective temperature exhibits some sensible time dependence and that it retains its connection with the partitioned phase space visited in aging. We underline the potential relevance of our numerical results for experimental studies of the fluctuation-dissipation relation in glassy systems.
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Affiliation(s)
- Nicoletta Gnan
- Dipartimento di Fisica, Università di Roma Sapienza, Roma, Italy.
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84
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Parisi G, Rizzo T. Critical dynamics in glassy systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012101. [PMID: 23410277 DOI: 10.1103/physreve.87.012101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2012] [Revised: 10/19/2012] [Indexed: 06/01/2023]
Abstract
Critical dynamics in various glass models, including those described by mode-coupling theory, is described by scale-invariant dynamical equations with a single nonuniversal quantity, i.e., the so-called parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular, the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.
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Affiliation(s)
- Giorgio Parisi
- Dipartimento Fisica, Università Sapienza, Piazzale A. Moro 2, I-00185 Rome, Italy
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85
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Abstract
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations.
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86
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Andreanov A, Müller M. Long-range quantum Ising spin glasses at t=0: gapless collective excitations and universality. PHYSICAL REVIEW LETTERS 2012; 109:177201. [PMID: 23215216 DOI: 10.1103/physrevlett.109.177201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2012] [Indexed: 06/01/2023]
Abstract
We solve the Sherrington-Kirkpatrick model in a transverse field Γ deep in its quantum glass phase at zero temperature. We show that the glass phase is critical everywhere, exhibiting collective excitations with a gapless Ohmic spectral function. Using an effective potential approach, we interpret the latter as arising from disordered collective excitations behaving like weakly coupled, underdamped oscillators. For a small transverse field Γ, the low-frequency spectrum takes a form independent of the fluctuation strength Γ.
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Affiliation(s)
- A Andreanov
- The Abdus Salam ICTP-Strada Costiera 11, 34151, Trieste, Italy
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87
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Nandi SK, Ramaswamy S. How do glassy domains grow? PHYSICAL REVIEW LETTERS 2012; 109:115702. [PMID: 23005646 DOI: 10.1103/physrevlett.109.115702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2012] [Indexed: 06/01/2023]
Abstract
We construct equations for the growth kinetics of structural glass within mode-coupling theory, through a nonstationary variant of the three-density correlator defined by G. Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)]. We solve a schematic form of the resulting equations to obtain the coarsening of the three-point correlator χ(3)(t,t(w)) as a function of waiting time t(w). For a quench into the glass, we find that χ(3) attains a peak value ∼t(w)(0.5) at t-t(w)∼t(w)(0.8), providing a theoretical basis for the numerical observations of Parisi [J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)]. The aging is not "simple": the t(w) dependence cannot be attributed to an evolving effective temperature.
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Affiliation(s)
- Saroj Kumar Nandi
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore-560 012, India.
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88
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Arenzon JJ, Sellitto M. Microscopic models of mode-coupling theory: the F12 scenario. J Chem Phys 2012; 137:084501. [PMID: 22938244 DOI: 10.1063/1.4746695] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the F(12) schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamical glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamical facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the F(13) schematic model.
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Affiliation(s)
- Jeferson J Arenzon
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
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89
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90
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Sen Gupta B, Das SP. Time dependent stretching of aging dynamics in a generalized hydrodynamic model for supercooled liquids. J Chem Phys 2012; 136:154506. [PMID: 22519335 DOI: 10.1063/1.4703898] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nonequilibrium dynamics and aging behavior of a supercooled liquid is investigated from an analysis of the correlation of density fluctuations at two different times. The dynamic correlation functions are computed by solving numerically the equations of nonlinear fluctuating hydrodynamics. The aging time dependence follows a modified stretched exponential form with a relaxation time which is dependent on the aging time. This is similar to the behavior seen in the aging data of dielectric response functions of a typical glass forming liquid.
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Affiliation(s)
- Bhaskar Sen Gupta
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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91
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Landy J, Rudnick J. Simplicity of the spherical spin-glass model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041127. [PMID: 22680439 DOI: 10.1103/physreve.85.041127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2011] [Revised: 02/10/2012] [Indexed: 06/01/2023]
Abstract
We revisit an approach to the replica-based analysis of the spherical spin-glass model that makes use of a mapping of the problem onto a one-dimensional interacting charge system. A saddle point approximation leads to the conclusion that the interaction between charges is irrelevant in the thermodynamic limit, and as a consequence, that there is no nontrivial correlation between replicas for this model. This allows us to show that quenched and annealed disorder averages agree for the spherical spin glass. We demonstrate this result within two different mathematical frameworks, and we also relate our analysis to the conclusions that follow from the replica symmetry ansatz.
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Affiliation(s)
- Jonathan Landy
- Materials Department, University of California, Santa Barbara, California 93106, USA.
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92
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Caltagirone F, Ferrari U, Leuzzi L, Parisi G, Ricci-Tersenghi F, Rizzo T. Critical slowing down exponents of mode coupling theory. PHYSICAL REVIEW LETTERS 2012; 108:085702. [PMID: 22463543 DOI: 10.1103/physrevlett.108.085702] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2011] [Indexed: 05/31/2023]
Abstract
A method is provided to compute the exponent parameter λ yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of λ in terms of third order coefficients of the action expansion or, equivalently, in terms of six point cumulants are provided. Applications are reported to a number of mean-field models: with hard and soft variables and both fully connected and dilute interactions. Comparisons with existing results for the Potts glass model, the random orthogonal model, hard and soft-spin Sherrington-Kirkpatrick, and p-spin models are presented.
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Affiliation(s)
- F Caltagirone
- Dipartamento Fisica, Università La Sapienza, Rome, Italy
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93
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Abstract
Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses.
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94
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Amir A, Borini S, Oreg Y, Imry Y. Huge (but finite) time scales in slow relaxations: beyond simple aging. PHYSICAL REVIEW LETTERS 2011; 107:186407. [PMID: 22107656 DOI: 10.1103/physrevlett.107.186407] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2011] [Indexed: 05/31/2023]
Abstract
Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the case-study example of porous silicon. The relaxations are experimentally observed even at room temperature over time scales of hours, and when a strong electric field is applied for a time tw, the ensuing relaxation depends on tw. We derive a theoretical curve and show that all experimental data collapse onto it with a single time scale as a fitting parameter. This time scale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not fine-tuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects.
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Affiliation(s)
- Ariel Amir
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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95
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Colombani J, Petit L, Ybert C, Barentin C. Probing the fluctuation-dissipation theorem in a Perrin-like experiment. PHYSICAL REVIEW LETTERS 2011; 107:130601. [PMID: 22026834 DOI: 10.1103/physrevlett.107.130601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2011] [Revised: 07/23/2011] [Indexed: 05/31/2023]
Abstract
In this Letter, we present a new experimental approach to investigate the effective temperature concept as a generalization of the fluctuation-dissipation theorem (FDT) for nonequilibrium systems. Simultaneous measurements of diffusion coefficient and sedimentation velocity of heavy colloids, embedded in a Laponite clay suspension, are performed with a fluorescence-recovery-based setup. This nonperturbative dual measurement, performed at a single time in a single sample, allows for a direct application of the FDT to the tracer velocity observable. It thus provides a well-defined derivation of the effective temperature in this ageing colloidal gel. For a wide range of concentrations and ageing times, we report no violation of the FDT, with effective temperature agreeing with bath temperature. This result is consistent with recent theoretical predictions on the coupling between the velocity observable and nonequilibrium gels dynamics.
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Affiliation(s)
- Jean Colombani
- Laboratoire de Physique de la Matière Condensée et Nanostructures, Université de Lyon, CNRS, UMR, Domaine scientifique de la Doua, Villeurbanne, France
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96
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Franz S, Parisi G, Ricci-Tersenghi F, Rizzo T. Field theory of fluctuations in glasses. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:102. [PMID: 21947902 DOI: 10.1140/epje/i2011-11102-0] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2011] [Accepted: 08/01/2011] [Indexed: 05/31/2023]
Abstract
We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments, we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be described through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.
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Affiliation(s)
- S Franz
- Laboratoire de Physique Théorique et Modèles Statistiques, CNRS et Université Paris-Sud 11, Bât. 100, 91405 Orsay Cedex, France.
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97
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Zhang M, Szamel G. Effective temperatures of a driven, strongly anisotropic Brownian system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061407. [PMID: 21797364 DOI: 10.1103/physreve.83.061407] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2011] [Indexed: 05/31/2023]
Abstract
We use Brownian dynamics computer simulations of a moderately dense colloidal system undergoing steady shear flow to investigate the uniqueness of the so-called effective temperature. We compare effective temperatures calculated from the fluctuation-dissipation ratios and from the linear response to a static, long-wavelength, external perturbation along two directions: the shear gradient direction and the vorticity direction. At high shear rates, when the system is strongly anisotropic, the fluctuation-dissipation-ratio-derived effective temperatures are approximately wave-vector independent, but the temperatures along the gradient direction are somewhat higher than those along the vorticity direction. The temperatures derived from the static linear response show the same dependence on the direction as those derived from the fluctuation-dissipation ratio. However, the former and the latter temperatures are different. Our results suggest that the presently used formulas for effective temperatures may not be applicable for strongly anisotropic, driven systems.
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Affiliation(s)
- Min Zhang
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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98
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Krzakala F, Zdeborová L. On melting dynamics and the glass transition. II. Glassy dynamics as a melting process. J Chem Phys 2011; 134:034513. [DOI: 10.1063/1.3506843] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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99
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Krzakala F, Zdeborová L. On melting dynamics and the glass transition. I. Glassy aspects of melting dynamics. J Chem Phys 2011; 134:034512. [DOI: 10.1063/1.3506841] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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100
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Ramírez-González P, Medina-Noyola M. General nonequilibrium theory of colloid dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061503. [PMID: 21230674 DOI: 10.1103/physreve.82.061503] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2009] [Revised: 10/27/2010] [Indexed: 05/30/2023]
Abstract
A nonequilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time-evolution equations of its mean value n(r,t) and of the covariance [Formula in text] of its fluctuations δn(r,t)=n(r,t)-n(r,t). These two coarse-grained equations involve a local mobility function b(r,t) which, in its turn, is written in terms of the memory function of the two-time correlation function [Formula in text]. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n(0)(r) and σ(0)(r,r') toward its equilibrium state characterized by the equilibrium local concentration profile n(eq)(r) and equilibrium covariance σ(eq)(r,r'). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities.
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Affiliation(s)
- Pedro Ramírez-González
- Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, San Luis Potosí, 78000 San Luis Potosí, Mexico
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