1
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Kurnosov A, Fernández-Alcázar LJ, Ramos A, Shapiro B, Kottos T. Optical Kinetic Theory of Nonlinear Multimode Photonic Networks. PHYSICAL REVIEW LETTERS 2024; 132:193802. [PMID: 38804952 DOI: 10.1103/physrevlett.132.193802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 04/04/2024] [Indexed: 05/29/2024]
Abstract
Recent experimental developments in multimode nonlinear photonic circuits (MMNPCs), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a nonequilibrium transport theory for these systems, when they are in contact with thermal reservoirs, is still terra incognita. Here, by combining Landauer and kinematics formalisms we develop a universal one-parameter scaling theory that describes the whole transport behavior from the ballistic to the diffusive regime, including both positive and negative optical temperature scenarios. We also derive a photonic version of the Wiedemann-Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPCs and may be useful for the design of all-optical cooling protocols.
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Affiliation(s)
- Arkady Kurnosov
- Department of Physics, Wave Transport in Complex Systems Laboratory, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Lucas J Fernández-Alcázar
- Institute for Modeling and Innovative Technology, IMIT (CONICET - UNNE), Corrientes W3404AAS, Argentina
- Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes W3404AAS, Argentina
| | - Alba Ramos
- Institute for Modeling and Innovative Technology, IMIT (CONICET - UNNE), Corrientes W3404AAS, Argentina
- Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes W3404AAS, Argentina
| | - Boris Shapiro
- Technion - Israel Institute of Technology, Technion City, Haifa 3200, Israel
| | - Tsampikos Kottos
- Department of Physics, Wave Transport in Complex Systems Laboratory, Wesleyan University, Middletown, Connecticut 06459, USA
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2
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Gotti G, Iubini S, Politi P. Condensation induced by coupled transport processes. Phys Rev E 2022; 106:054158. [PMID: 36559399 DOI: 10.1103/physreve.106.054158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
Several lattice models display a condensation transition in real space when the density of a suitable order parameter exceeds a critical value. We consider one of such models with two conservation laws, in a onedimensional open setup where the system is attached to two external reservoirs. Both reservoirs impose subcritical boundary conditions at the chain ends. When such boundary conditions are equal, the system is in equilibrium below the condensation threshold and no condensate can appear. Instead, when the system is kept out of equilibrium, localization may arise in an internal portion of the lattice. We discuss the origin of this phenomenon, the relevance of the number of conservation laws, and the effect of the pinning of the condensate on the dynamics of the out-of-equilibrium state.
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Affiliation(s)
- Gabriele Gotti
- Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Stefano Iubini
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Paolo Politi
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
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3
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Benenti G, Casati G, Marchesoni F, Wang J. Autonomous circular heat engine. Phys Rev E 2022; 106:044104. [PMID: 36397467 DOI: 10.1103/physreve.106.044104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
A dynamical model of a highly efficient heat engine is proposed, where an applied temperature difference maintains the motion of particles around the circuit consisting of two asymmetric narrow channels, in one of which the current flows against the applied thermodynamic forces. Numerical simulations and linear-response analysis suggest that, in the absence of frictional losses, the Carnot efficiency can be achieved in the thermodynamic limit.
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Affiliation(s)
- Giuliano Benenti
- Dipartimento di Scienza e Alta Technologia, Center for Nonlinear and Complex Systems, Universitâ degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
- NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Giulio Casati
- Dipartimento di Scienza e Alta Technologia, Center for Nonlinear and Complex Systems, Universitâ degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário - Lagoa Nova, CP. 1613, Natal, Rio Grande Do Norte 59078-970, Brazil
| | - Fabio Marchesoni
- Department of Physics, University of Camerino, 61032 Camerino, Italy
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jiao Wang
- Department of Physics and Key Laboratory of Low Dimensional Condensed Matter Physics (Department of Education of Fujian Province), Xiamen University, Xiamen 361005, Fujian, China
- Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, Gansu, China
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4
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Xiong D, Wang J. Subdiffusive energy transport and antipersistent correlations due to the scattering of phonons and discrete breathers. Phys Rev E 2022; 106:L032201. [PMID: 36266887 DOI: 10.1103/physreve.106.l032201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
While there are many physical processes showing subdiffusion and some useful particle models for understanding the underlying mechanisms have been established, a systematic study of subdiffusive energy transport is still lacking. Here we present convincing evidence that, in the range of system size investigated, the energy subdiffusion can take place in a Hamiltonian lattice system with both harmonic nearest-neighbor and anharmonic long-range interactions. In particular, we show that the interaction range dependence of antipersistent energy-current correlations are relevant to this special type of energy subdiffusion. The underlying mechanisms are related to the various scattering processes of phonons and discrete breathers. Our results shed light on understanding the extremely slow energy transport.
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Affiliation(s)
- Daxing Xiong
- MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
| | - Jianjin Wang
- Department of Physics, Jiangxi Science and Technology Normal University, Nanchang 330013, Jiangxi, China
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5
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Onorato M, Dematteis G, Proment D, Pezzi A, Ballarin M, Rondoni L. Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach. Phys Rev E 2022; 105:014206. [PMID: 35193220 DOI: 10.1103/physreve.105.014206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 12/22/2021] [Indexed: 11/07/2022]
Abstract
We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behavior on a shorter timescale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation.
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Affiliation(s)
- M Onorato
- Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy.,Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino, Italy
| | - G Dematteis
- Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - D Proment
- School of Mathematics, University of East Anglia, Norwich Research Park, NR47TJ Norwich, United Kingdom
| | - A Pezzi
- Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy
| | - M Ballarin
- Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy
| | - L Rondoni
- Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino, Italy.,Dipartimento di Scienze Matematiche, Politecnico di Torino, I-10129 Torino, Italy
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6
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Chatterjee AK, Kulkarni M, Kundu A. Dynamical regimes of finite-temperature discrete nonlinear Schrödinger chain. Phys Rev E 2021; 104:044136. [PMID: 34781584 DOI: 10.1103/physreve.104.044136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 10/12/2021] [Indexed: 11/07/2022]
Abstract
We show that the one-dimensional discrete nonlinear Schrödinger chain (DNLS) at finite temperature has three different dynamical regimes (ultralow-, low-, and high-temperature regimes). This has been established via (i) one-point macroscopic thermodynamic observables (temperature T, energy density ε, and the relationship between them), (ii) emergence and disappearance of an additional almost conserved quantity (total phase difference), and (iii) classical out-of-time-ordered correlators and related quantities (butterfly speed and Lyapunov exponents). The crossover temperatures T_{l-ul} (between low- and ultra-low-temperature regimes) and T_{h-l} (between the high- and low-temperature regimes) extracted from these three different approaches are consistent with each other. The analysis presented here is an important step forward toward the understanding of DNLS which is ubiquitous in many fields and has a nonseparable Hamiltonian form. Our work also shows that the different methods used here can serve as important tools to identify dynamical regimes in other interacting many-body systems.
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Affiliation(s)
- Amit Kumar Chatterjee
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Manas Kulkarni
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Anupam Kundu
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
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7
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Mithun T, Maluckov A, Manda BM, Skokos C, Bishop A, Saxena A, Khare A, Kevrekidis PG. Thermalization in the one-dimensional Salerno model lattice. Phys Rev E 2021; 103:032211. [PMID: 33862787 DOI: 10.1103/physreve.103.032211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 03/04/2021] [Indexed: 11/07/2022]
Abstract
The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.
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Affiliation(s)
- Thudiyangal Mithun
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - Aleksandra Maluckov
- Vinca Institute of Nuclear Sciences, University of Belgrade, National Institute of the Republic of Serbia, P.O.B. 522, 11001 Belgrade, Serbia.,Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34051, S. Korea
| | - Bertin Many Manda
- Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 Cape Town, South Africa
| | - Charalampos Skokos
- Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 Cape Town, South Africa
| | - Alan Bishop
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Avadh Saxena
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Avinash Khare
- Department of Physics, Savitribai Phule Pune University, Pune 411007, India
| | - Panayotis G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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8
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Wang J, Casati G, Benenti G. Inverse Currents in Hamiltonian Coupled Transport. PHYSICAL REVIEW LETTERS 2020; 124:110607. [PMID: 32242708 DOI: 10.1103/physrevlett.124.110607] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
The occurrence of an inverse current, where the sign of the induced current is opposite to the applied force, is a highly counterintuitive phenomenon. We show that inverse currents in coupled transport (ICC) of energy and particle can occur in a one-dimensional interacting Hamiltonian system when its equilibrium state is perturbed by coupled thermodynamic forces. This seemingly paradoxical result is possible due to the self-organization occurring in the system in response to the applied forces.
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Affiliation(s)
- Jiao Wang
- Department of Physics and Key Laboratory of Low Dimensional Condensed Matter Physics (Department of Education of Fujian Province), Xiamen University, Xiamen 361005, Fujian, China
| | - Giulio Casati
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário-Lagoa Nova, CP. 1613, Natal, Rio Grande Do Norte 59078-970, Brazil
| | - Giuliano Benenti
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
- NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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9
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Dephasing-Assisted Macrospin Transport. ENTROPY 2020; 22:e22020210. [PMID: 33285985 PMCID: PMC7516640 DOI: 10.3390/e22020210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Revised: 02/07/2020] [Accepted: 02/10/2020] [Indexed: 11/29/2022]
Abstract
Transport phenomena are ubiquitous in physics, and it is generally understood that the environmental disorder and noise deteriorates the transfer of excitations. There are, however, cases in which transport can be enhanced by fluctuations. In the present work, we show, by means of micromagnetics simulations, that transport efficiency in a chain of classical macrospins can be greatly increased by an optimal level of dephasing noise. We also demonstrate the same effect in a simplified model, the dissipative Discrete Nonlinear Schrödinger equation, subject to phase noise. Our results point towards the realization of a large class of magnonics and spintronics devices, where disorder and noise can be used to enhance spin-dependent transport efficiency.
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10
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Miceli F, Baldovin M, Vulpiani A. Statistical mechanics of systems with long-range interactions and negative absolute temperature. Phys Rev E 2019; 99:042152. [PMID: 31108672 DOI: 10.1103/physreve.99.042152] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2018] [Indexed: 11/07/2022]
Abstract
A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex function of the total energy, meaning that ensemble equivalence is violated in a negative-temperature regime. The equilibrium properties of the model are then investigated by molecular dynamics simulations: first, the caloric curve is reconstructed for the microcanonical ensemble and compared to the analytical prediction, and a generalized Maxwell-Boltzmann distribution for the momenta is observed; then the nonequivalence between the microcanonical and canonical descriptions is explicitly shown. Moreover, the validity of the Fluctuation-Dissipation Theorem is verified through a numerical study, also at negative temperature and in the region where the two ensembles are nonequivalent.
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Affiliation(s)
- Fabio Miceli
- Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 5, 00185, Rome, Italy
| | - Marco Baldovin
- Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 5, 00185, Rome, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 5, 00185, Rome, Italy.,Centro Linceo Interdisciplinare "B. Segre," Accademia dei Lincei Via della Lungara 10, 00165, Rome, Italy
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11
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Iubini S, Chirondojan L, Oppo GL, Politi A, Politi P. Dynamical Freezing of Relaxation to Equilibrium. PHYSICAL REVIEW LETTERS 2019; 122:084102. [PMID: 30932580 DOI: 10.1103/physrevlett.122.084102] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Revised: 01/23/2019] [Indexed: 06/09/2023]
Abstract
We provide evidence of an extremely slow thermalization occurring in the discrete nonlinear Schrödinger model. At variance with many similar processes encountered in statistical mechanics-typically ascribed to the presence of (free) energy barriers-here the slowness has a purely dynamical origin: it is due to the presence of an adiabatic invariant, which freezes the dynamics of a tall breather. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the nonergodic behavior recently observed in the negative-temperature region of the discrete nonlinear Schrödinger equation.
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Affiliation(s)
- Stefano Iubini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
| | - Liviu Chirondojan
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Antonio Politi
- Institute for Complex Systems and Mathematical Biology & SUPA University of Aberdeen, Aberdeen AB24 3UE, Scotland, United Kingdom
| | - Paolo Politi
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
- INFN Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
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12
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Mithun T, Kati Y, Danieli C, Flach S. Weakly Nonergodic Dynamics in the Gross-Pitaevskii Lattice. PHYSICAL REVIEW LETTERS 2018; 120:184101. [PMID: 29775355 DOI: 10.1103/physrevlett.120.184101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2017] [Indexed: 06/08/2023]
Abstract
The microcanonical Gross-Pitaevskii (also known as the semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm densities. The grand canonical Gibbs distribution fails to describe a part of the density space, due to the boundedness of its kinetic energy spectrum. We define Poincaré equilibrium manifolds and compute the statistics of microcanonical excursion times off them. The tails of the distribution functions quantify the proximity of the many-body dynamics to a weakly nonergodic phase, which occurs when the average excursion time is infinite. We find that a crossover to weakly nonergodic dynamics takes place inside the non-Gibbs phase, being unnoticed by the largest Lyapunov exponent. In the ergodic part of the non-Gibbs phase, the Gibbs distribution should be replaced by an unknown modified one. We relate our findings to the corresponding integrable limit, close to which the actions are interacting through a short range coupling network.
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Affiliation(s)
- Thudiyangal Mithun
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34051, Korea
| | - Yagmur Kati
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34051, Korea
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Republic of Korea
| | - Carlo Danieli
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34051, Korea
| | - Sergej Flach
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34051, Korea
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13
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Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations. Sci Rep 2018; 8:5329. [PMID: 29593230 PMCID: PMC5871775 DOI: 10.1038/s41598-018-23719-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2018] [Accepted: 03/20/2018] [Indexed: 11/08/2022] Open
Abstract
For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-β (FPU-β) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-β lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-β lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-β lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.
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14
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Borlenghi S, Iubini S, Lepri S, Fransson J. Entropy production for complex Langevin equations. Phys Rev E 2018; 96:012150. [PMID: 29347077 DOI: 10.1103/physreve.96.012150] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 11/07/2022]
Abstract
We study irreversible processes for nonlinear oscillators networks described by complex-valued Langevin equations that account for coupling to different thermochemical baths. Dissipation is introduced via non-Hermitian terms in the Hamiltonian of the model. We apply the stochastic thermodynamics formalism to compute explicit expressions for the entropy production rates. We discuss in particular the nonequilibrium steady states of the network characterized by a constant production rate of entropy and flows of energy and particle currents. For two specific examples, a one-dimensional chain and a dimer, numerical calculations are presented. The role of asymmetric coupling among the oscillators on the entropy production is illustrated.
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Affiliation(s)
- Simone Borlenghi
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
| | - Stefano Iubini
- Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1 I-50019, Sesto Fiorentino, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1 I-50019, Sesto Fiorentino, Italy
| | - Stefano Lepri
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1 I-50019, Sesto Fiorentino, Italy.,Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10 I-50019 Sesto Fiorentino, Italy
| | - Jonas Fransson
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
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15
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16
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Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains. ACTA ACUST UNITED AC 2016. [DOI: 10.1007/978-3-319-29261-8_3] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
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17
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Borlenghi S. Gauge invariance and geometric phase in nonequilibrium thermodynamics. Phys Rev E 2016; 93:012133. [PMID: 26871050 DOI: 10.1103/physreve.93.012133] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2015] [Indexed: 11/07/2022]
Abstract
We show the link between U(1) lattice gauge theories and the off-equilibrium thermodynamics of a large class of nonlinear oscillators networks. The coupling between the oscillators plays the role of a gauge field, or connection, on the network. The thermodynamical forces that drive energy flows are expressed in terms of the curvature of the connection, analogous to a geometric phase. The model, which holds both close and far from equilibrium, predicts the existence of persistent energy and particle currents circulating in closed loops through the network. The predictions are confirmed by numerical simulations. Possible extension of the theory and experimental applications to nanoscale devices are briefly discussed.
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Affiliation(s)
- Simone Borlenghi
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
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18
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Borlenghi S, Iubini S, Lepri S, Chico J, Bergqvist L, Delin A, Fransson J. Energy and magnetization transport in nonequilibrium macrospin systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012116. [PMID: 26274133 DOI: 10.1103/physreve.92.012116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2015] [Indexed: 06/04/2023]
Abstract
We investigate numerically the magnetization dynamics of an array of nanodisks interacting through the magnetodipolar coupling. In the presence of a temperature gradient, the chain reaches a nonequilibrium steady state where energy and magnetization currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schrödinger (DNLS) equation. This model makes transparent the transport properties of the system and allows for a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model.
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Affiliation(s)
- Simone Borlenghi
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Stefano Iubini
- Centre de Biophysique Moléculaire (CBM), CNRS-UPR 4301 Rue Charles Sadron, F-45071 Orléans, France
| | - Stefano Lepri
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Jonathan Chico
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
| | - Lars Bergqvist
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Anna Delin
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Jonas Fransson
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
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Borlenghi S, Iubini S, Lepri S, Bergqvist L, Delin A, Fransson J. Coherent energy transport in classical nonlinear oscillators: An analogy with the Josephson effect. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:040102. [PMID: 25974425 DOI: 10.1103/physreve.91.040102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2014] [Indexed: 06/04/2023]
Abstract
By means of a simple theoretical model and numerical simulations, we demonstrate the presence of persistent energy currents in a lattice of classical nonlinear oscillators with uniform temperature and chemical potential. In analogy with the well-known Josephson effect, the currents are proportional to the sine of the phase differences between the oscillators. Our results elucidate general aspects of nonequilibrium thermodynamics and point towards a way to practically control transport phenomena in a large class of systems. We apply the model to describe the phase-controlled spin-wave current in a bilayer nanopillar.
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Affiliation(s)
- Simone Borlenghi
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Stefano Iubini
- Centre de Biophysique Moléculaire (CBM), CNRS-UPR 4301, Rue Charles Sadron, F-45071 Orléans, France
| | - Stefano Lepri
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Unità Operativa di Firenze, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Lars Bergqvist
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Anna Delin
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Jonas Fransson
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
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Iubini S, Lepri S, Livi R, Politi A. Boundary-induced instabilities in coupled oscillators. PHYSICAL REVIEW LETTERS 2014; 112:134101. [PMID: 24745424 DOI: 10.1103/physrevlett.112.134101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2014] [Indexed: 06/03/2023]
Abstract
A novel class of nonequilibrium phase transitions at zero temperature is found in chains of nonlinear oscillators. For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schrödinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a nontrivial interfacial region where the kinetic temperature is finite. Dynamics in such a supercritical state displays anomalous chaotic properties whereby some observables are nonextensive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the temperature profile is still nonmonotonic.
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Affiliation(s)
- Stefano Iubini
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Stefano Lepri
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Roberto Livi
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Antonio Politi
- Institute for Complex Systems and Mathematical Biology & SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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Basko DM. Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022921. [PMID: 25353559 DOI: 10.1103/physreve.89.022921] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2013] [Indexed: 06/04/2023]
Abstract
We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.
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Affiliation(s)
- D M Basko
- Université Grenoble 1/CNRS, LPMMC UMR 5493, 25 rue des Martyrs, 38042 Grenoble, France
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Borlenghi S, Wang W, Fangohr H, Bergqvist L, Delin A. Designing a spin-Seebeck diode. PHYSICAL REVIEW LETTERS 2014; 112:047203. [PMID: 24580487 DOI: 10.1103/physrevlett.112.047203] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Indexed: 06/03/2023]
Abstract
Using micromagnetic simulations, we have investigated spin dynamics in a spin-valve bilayer in the presence of a thermal gradient. The direction and the intensity of the gradient allow us to excite the spin wave modes of each layer selectively. This permits us to synchronize the magnetization precession of the two layers and to rectify the flows of energy and magnetization through the system. Our study yields promising opportunities for applications in spin caloritronics and nanophononics devices.
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Affiliation(s)
- Simone Borlenghi
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden
| | - Weiwei Wang
- Engineering and the Environment, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Hans Fangohr
- Engineering and the Environment, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Lars Bergqvist
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden and SeRC (Swedish e-Science Research Center), KTH, SE-10044 Stockholm, Sweden
| | - Anna Delin
- Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology, SE-16440 Kista, Sweden and SeRC (Swedish e-Science Research Center), KTH, SE-10044 Stockholm, Sweden and Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
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