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Caspers J, Krüger M. Nonlinear Langevin functionals for a driven probe. J Chem Phys 2024; 161:124109. [PMID: 39319648 DOI: 10.1063/5.0227674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2024] [Accepted: 09/04/2024] [Indexed: 09/26/2024] Open
Abstract
When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism. (i) For a particle driven with the prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. (ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third- or second-order response, respectively.
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Affiliation(s)
- Juliana Caspers
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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2
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Sazhin A, Gladilin VN, Erglis A, Hellmann G, Vewinger F, Weitz M, Wouters M, Schmitt J. Observation of nonlinear response and Onsager regression in a photon Bose-Einstein condensate. Nat Commun 2024; 15:4730. [PMID: 38830905 PMCID: PMC11148057 DOI: 10.1038/s41467-024-49064-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 05/22/2024] [Indexed: 06/05/2024] Open
Abstract
The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas, and, moreover, demonstrates it in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response.
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Affiliation(s)
| | | | - Andris Erglis
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany
| | - Göran Hellmann
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany
- Leibniz Institute of Photonic Technology, Jena, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany
| | | | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany.
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3
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Asheichyk K, Fuchs M, Krüger M. Brownian systems perturbed by mild shear: comparing response relations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:405101. [PMID: 34139676 DOI: 10.1088/1361-648x/ac0c3c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 06/17/2021] [Indexed: 06/12/2023]
Abstract
We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.
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Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- Department of Theoretical Physics and Astrophysics, Belarusian State University, 5 Babruiskaya St., 220006 Minsk, Belarus
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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4
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Holsten T, Krüger M. Thermodynamic nonlinear response relation. Phys Rev E 2021; 103:032116. [PMID: 33862688 DOI: 10.1103/physreve.103.032116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 02/16/2021] [Indexed: 11/07/2022]
Abstract
The fluctuation-dissipation theorem connects equilibrium to mildly (linearly) perturbed situations in a thermodynamic manner: It involves the observable of interest and the entropy production caused by the perturbation. We derive a relation which connects responses of arbitrary order in perturbation strength to correlations of entropy production of lower order, thereby extending the fluctuation-dissipation theorem to cases far from equilibrium in a thermodynamic way. The relation is validated and studied for a four-state model which is coarse-grained to a non-Markovian two-state model.
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Affiliation(s)
- Tristan Holsten
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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Sarracino A, Vulpiani A. On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems. CHAOS (WOODBURY, N.Y.) 2019; 29:083132. [PMID: 31472486 DOI: 10.1063/1.5110262] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 08/08/2019] [Indexed: 06/10/2023]
Abstract
We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.
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Affiliation(s)
- A Sarracino
- Dipartimento di Ingegneria, Università della Campania "L. Vanvitelli," via Roma 29, 81031 Aversa (CE), Italy
| | - A Vulpiani
- Dipartimento di Fisica, Università Sapienza-p.le A. Moro 2, 00185 Roma, Italy
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6
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Gao CY, Limmer DT. Nonlinear transport coefficients from large deviation functions. J Chem Phys 2019; 151:014101. [PMID: 31272161 DOI: 10.1063/1.5110507] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here, we introduce a way to compute arbitrarily high order transport coefficients of stochastic systems, using the framework of large deviation theory. Leveraging time reversibility in the microscopic dynamics, we relate nonlinear response to equilibrium multitime correlation functions among both time reversal symmetric and asymmetric observables, which can be evaluated from derivatives of large deviation functions. This connection establishes a thermodynamiclike relation for nonequilibrium response and provides a practical route to its evaluation, as large deviation functions are amenable to importance sampling. We demonstrate the generality and efficiency of this method in predicting transport coefficients in single particle systems and an interacting system exhibiting thermal rectification.
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Affiliation(s)
- Chloe Ya Gao
- Department of Chemistry, University of California, Berkeley, California 94609, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94609, USA
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Maes C, Netočný K. Nonequilibrium corrections to gradient flow. CHAOS (WOODBURY, N.Y.) 2019; 29:073109. [PMID: 31370412 DOI: 10.1063/1.5098055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2019] [Accepted: 06/29/2019] [Indexed: 06/10/2023]
Abstract
The force on a probe induced by a nonequilibrium medium is in general nongradient. We detail the mechanism of this feature via nonequilibrium response theory. The emergence of nongradient forces is due to a systematic "twist" of the excess frenesy with respect to the entropy flux, in response to changes in the coupling or in the position of the probe in the nonequilibrium medium.
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Affiliation(s)
- Christian Maes
- Instituut voor Theoretische Fysica, KU Leuven, 3001 Leuven, Belgium
| | - Karel Netočný
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
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Asheichyk K, Solon AP, Rohwer CM, Krüger M. Response of active Brownian particles to shear flow. J Chem Phys 2019; 150:144111. [DOI: 10.1063/1.5086495] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
| | - Alexandre P. Solon
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matiére Condensée, LPTMC, F-75005 Paris, France
| | - Christian M. Rohwer
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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Cecconi F, Puglisi A, Sarracino A, Vulpiani A. Anomalous mobility of a driven active particle in a steady laminar flow. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:264002. [PMID: 29762125 DOI: 10.1088/1361-648x/aac4f0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale [Formula: see text]. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ([Formula: see text]) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite [Formula: see text] a more complex force-velocity relation can be observed.
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Affiliation(s)
- F Cecconi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
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10
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Basu U, Helden L, Krüger M. Extrapolation to Nonequilibrium from Coarse-Grained Response Theory. PHYSICAL REVIEW LETTERS 2018; 120:180604. [PMID: 29775331 DOI: 10.1103/physrevlett.120.180604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Revised: 02/12/2018] [Indexed: 06/08/2023]
Abstract
Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.
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Affiliation(s)
- Urna Basu
- SISSA-International School for Advanced Studies and INFN, 34136 Trieste, Italy
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Laurent Helden
- 2. Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, 70550 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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11
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Garrahan JP. Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables. Phys Rev E 2017; 95:032134. [PMID: 28415371 DOI: 10.1103/physreve.95.032134] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 06/07/2023]
Abstract
Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.
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Affiliation(s)
- Juan P Garrahan
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Krüger M, Maes C. The modified Langevin description for probes in a nonlinear medium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:064004. [PMID: 28002047 DOI: 10.1088/1361-648x/29/6/064004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is no longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.
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Affiliation(s)
- Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, Stuttgart, Germany. Max Planck Institute for Intelligent Systems, Stuttgart, Germany
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Seyboldt R, Merger D, Coupette F, Siebenbürger M, Ballauff M, Wilhelm M, Fuchs M. Divergence of the third harmonic stress response to oscillatory strain approaching the glass transition. SOFT MATTER 2016; 12:8825-8832. [PMID: 27752694 DOI: 10.1039/c6sm01616b] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The leading nonlinear stress response in a periodically strained concentrated colloidal dispersion is studied experimentally and by theory. A thermosensitive microgel dispersion serves as well-characterized glass-forming model, where the stress response at the first higher harmonic frequency (3ω for strain at frequency ω) is investigated in the limit of small amplitude. The intrinsic nonlinearity at the third harmonic exhibits a scaling behavior which has a maximum in an intermediate frequency window and diverges when approaching the glass transition. It captures the (in-) stability of the transient elastic structure. Elastic stresses in-phase with the third power of the strain dominate the scaling. Our results qualitatively differ from previously derived scaling behavior in dielectric spectroscopy of supercooled molecular liquids. This might indicate a dependence of the nonlinear response on the symmetry of the external driving under time reversal.
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Affiliation(s)
- Rabea Seyboldt
- Department of Physics, Universität Konstanz, 78464 Konstanz, Germany. and Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Dimitri Merger
- Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Fabian Coupette
- Department of Physics, Universität Konstanz, 78464 Konstanz, Germany.
| | - Miriam Siebenbürger
- Institute Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany
| | - Matthias Ballauff
- Institute Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany
| | - Manfred Wilhelm
- Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Matthias Fuchs
- Department of Physics, Universität Konstanz, 78464 Konstanz, Germany.
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments. Phys Rev E 2016; 93:032128. [PMID: 27078313 DOI: 10.1103/physreve.93.032128] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2015] [Indexed: 06/05/2023]
Abstract
We study analytically the dynamics and the microstructural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active microrheology experiments, we consider here a minimal model comprising a geometrically confined lattice system (a two-dimensional striplike or a three-dimensional capillary-like system) populated by two types of hard-core particles with stochastic dynamics (a tracer particle driven by a constant external force and bath particles moving completely at random). Resorting to a decoupling scheme, which permits us to go beyond the linear-response approximation (Stokes regime) for arbitrary densities of the lattice gas particles, we determine the force-velocity relation for the tracer particle and the stationary density profiles of the host medium particles around it. These results are validated a posteriori by extensive numerical simulations for a wide range of parameters. Our theoretical analysis reveals two striking features: (a) We show that, under certain conditions, the terminal velocity of the driven tracer particle is a nonmonotonic function of the force, so in some parameter range the differential mobility becomes negative, and (b) the biased particle drives the whole system into a nonequilibrium steady state with a stationary particle density profile past the tracer, which decays exponentially, in sharp contrast with the behavior observed for unbounded lattices, where an algebraic decay is known to take place.
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Affiliation(s)
- O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - P Illien
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - G Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - A Sarracino
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
| | - R Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
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