DOI

1

Population aging through survival of the fit and stable - Brotto, Tommaso and Bunin, Guy and Kurchan, Jorge

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT , (2016)

Abstract : Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a chemostat or a Petri dish. Our aim is to show that mutation rate and fitness become more correlated, even if they are completely uncorrelated for an isolated individual, underlining the fact that the interaction induced by limitation of resources is by itself effcient for generating collective effects.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT , (2016)

LPS

Abstract : Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a chemostat or a Petri dish. Our aim is to show that mutation rate and fitness become more correlated, even if they are completely uncorrelated for an isolated individual, underlining the fact that the interaction induced by limitation of resources is by itself effcient for generating collective effects.

DOI

2

Approximate scale invariance in particle systems: A large-dimensional justification - Maimbourg, Thibaud and Kurchan, Jorge

EPL 114, (2016)

Abstract : Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different ``isomorphic'' sets of temperatures and densities. In a recent series of works, it has been argued that such correspondences hold to a surprisingly good approximation in a much more general class of potentials, an observation that summarizes many properties that have been observed in the past. In this paper we show that such relations are exact in high-dimensional liquids and glasses, a limit in which the conditions for these mappings to hold become transparent. The special role played by the exponential potential is also confirmed. Copyright (C) EPLA, 2016

EPL 114, (2016)

LPS

Abstract : Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different ``isomorphic'' sets of temperatures and densities. In a recent series of works, it has been argued that such correspondences hold to a surprisingly good approximation in a much more general class of potentials, an observation that summarizes many properties that have been observed in the past. In this paper we show that such relations are exact in high-dimensional liquids and glasses, a limit in which the conditions for these mappings to hold become transparent. The special role played by the exponential potential is also confirmed. Copyright (C) EPLA, 2016

DOI

3

Large deviations, metastability and selection - Kurchan, Jorge

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 418, 170-188 (2015)

Abstract : In this note I introduce some techniques to treat systems in contact with (stochastic) thermal baths. The methods and the level of rigour are those of theoretical physics. (C) 2014 Elsevier B.V. All rights reserved.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 418, 170-188 (2015)

LPS

Abstract : In this note I introduce some techniques to treat systems in contact with (stochastic) thermal baths. The methods and the level of rigour are those of theoretical physics. (C) 2014 Elsevier B.V. All rights reserved.

DOI

4

Stochastic Perturbation of Integrable Systems: A Window to Weakly Chaotic Systems - Khanh-Dang Nguyen Thu Lam and Kurchan, Jorge

JOURNAL OF STATISTICAL PHYSICS 156, 619-646 (2014)

Abstract : Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in hydrodynamics. We develop expressions for the Lyapunov exponents for the cases of white and colored noise. The situation described here being `multi-resonance'aEuro''by nature well beyond the Kolmogorov-Arnold-Moser regime, it offers an analytic glimpse on the regime in which many near-integrable systems, such as some planetary systems, find themselves in practice. We show with the aid of a simple example, how one may model in some cases weakly chaotic deterministic systems by a stochastically perturbed one, with good qualitative results.

JOURNAL OF STATISTICAL PHYSICS 156, 619-646 (2014)

LPS

Abstract : Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in hydrodynamics. We develop expressions for the Lyapunov exponents for the cases of white and colored noise. The situation described here being `multi-resonance'aEuro''by nature well beyond the Kolmogorov-Arnold-Moser regime, it offers an analytic glimpse on the regime in which many near-integrable systems, such as some planetary systems, find themselves in practice. We show with the aid of a simple example, how one may model in some cases weakly chaotic deterministic systems by a stochastically perturbed one, with good qualitative results.

DOI

5

Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution - Charbonneau, Patrick and Kurchan, Jorge and Parisi, Giorgio and Urbani, Pierfrancesco and Zamponi, Francesco

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT , (2014)

Abstract : In the first part of this paper, we derive the general replica equations that describe infinite-dimensional hard spheres at any level of replica symmetry breaking (RSB) and in particular in the fullRSB scheme. We show that these equations are formally very similar to the ones that have been derived for spin glass models, thus showing that the analogy between spin glasses and structural glasses conjectured by Kirkpatrick, Thirumalai and Wolynes is realized in a strong sense in the mean-field limit. We also suggest how the computation could be generalized in an approximate way to finite-dimensional hard spheres. In the second part of the paper, we discuss the solution of these equations and we derive from it a number of physical predictions. We show that, below the Gardner transition where the 1RSB solution becomes unstable, a fullRSB phase exists and we locate the boundary of the fullRSB phase. Most importantly, we show that the fullRSB solution predicts correctly that jammed packings are iso-static, and allows one to compute analytically the critical exponents associated with the jamming transition, which are missed by the 1RSB solution. We show that these predictions compare very well with numerical results.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT , (2014)

LPS

Abstract : In the first part of this paper, we derive the general replica equations that describe infinite-dimensional hard spheres at any level of replica symmetry breaking (RSB) and in particular in the fullRSB scheme. We show that these equations are formally very similar to the ones that have been derived for spin glass models, thus showing that the analogy between spin glasses and structural glasses conjectured by Kirkpatrick, Thirumalai and Wolynes is realized in a strong sense in the mean-field limit. We also suggest how the computation could be generalized in an approximate way to finite-dimensional hard spheres. In the second part of the paper, we discuss the solution of these equations and we derive from it a number of physical predictions. We show that, below the Gardner transition where the 1RSB solution becomes unstable, a fullRSB phase exists and we locate the boundary of the fullRSB phase. Most importantly, we show that the fullRSB solution predicts correctly that jammed packings are iso-static, and allows one to compute analytically the critical exponents associated with the jamming transition, which are missed by the 1RSB solution. We show that these predictions compare very well with numerical results.

DOI

6

Exact Theory of Dense Amorphous Hard Spheres in High Dimension. II. The High Density Regime and the Gardner Transition - Kurchan, Jorge and Parisi, Giorgio and Urbani, Pierfrancesco and Zamponi, Francesco

JOURNAL OF PHYSICAL CHEMISTRY B 117, 12979-12994 (2013)

Abstract : We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the random first order transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis and a further transition at higher pressures in which a glassy structure of microstates is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Microstates that are small excitations of an amorphous matrix-separated by low entropic or energetic barriers-thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.

JOURNAL OF PHYSICAL CHEMISTRY B 117, 12979-12994 (2013)

LPS

Abstract : We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the random first order transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis and a further transition at higher pressures in which a glassy structure of microstates is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Microstates that are small excitations of an amorphous matrix-separated by low entropic or energetic barriers-thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.

DOI

7

Density of states of colloidal glasses and supercooled liquids - Ghosh, Antina and Mari, Romain and Chikkadi, Vijayakumar and Schall, Peter and Kurchan, Jorge and Bonn, Daniel

SOFT MATTER 6, 3082-3090 (2010)

Abstract : The glass transition is perhaps the greatest unsolved problem in condensed matter physics: the main question is how to reconcile the liquid-like structure with solid-like mechanical properties. In solids, structure and mechanics are related directly through the vibrational density of states of the material. Here, we obtain for the first time the density of states of colloidal glasses and supercooled liquids from a normal-mode analysis of particle displacements measured using confocal microscopy. We find that the spectrum of the (non-linear) vibrations has many `soft', low-frequency modes, more abundant and very different in nature from the usual acoustic vibrations of ordinary solids. This results in an anomalous low-frequency peak in the density of states which approaches zero frequency as one goes deeper into the glass. The observed soft modes are due to collective `swirling' particle motions, that extend over surprisingly long length scales.

SOFT MATTER 6, 3082-3090 (2010)

LPS

Abstract : The glass transition is perhaps the greatest unsolved problem in condensed matter physics: the main question is how to reconcile the liquid-like structure with solid-like mechanical properties. In solids, structure and mechanics are related directly through the vibrational density of states of the material. Here, we obtain for the first time the density of states of colloidal glasses and supercooled liquids from a normal-mode analysis of particle displacements measured using confocal microscopy. We find that the spectrum of the (non-linear) vibrations has many `soft', low-frequency modes, more abundant and very different in nature from the usual acoustic vibrations of ordinary solids. This results in an anomalous low-frequency peak in the density of states which approaches zero frequency as one goes deeper into the glass. The observed soft modes are due to collective `swirling' particle motions, that extend over surprisingly long length scales.

DOI

8

Density of States of Colloidal Glasses - Ghosh, Antina and Chikkadi, Vijayakumar K. and Schall, Peter and Kurchan, Jorge and Bonn, Daniel

PHYSICAL REVIEW LETTERS 104, (2010)

Abstract : Glasses are structurally liquidlike, but mechanically solidlike. Most attempts to understand glasses start from liquid state theory. Here we take the opposite point of view, and use concepts from solid state physics. We determine the vibrational modes of a colloidal glass experimentally, and find soft low-frequency modes that are very different in nature from the usual acoustic vibrations of ordinary solids. These modes extend over surprisingly large length scales.

PHYSICAL REVIEW LETTERS 104, (2010)

LPS

Abstract : Glasses are structurally liquidlike, but mechanically solidlike. Most attempts to understand glasses start from liquid state theory. Here we take the opposite point of view, and use concepts from solid state physics. We determine the vibrational modes of a colloidal glass experimentally, and find soft low-frequency modes that are very different in nature from the usual acoustic vibrations of ordinary solids. These modes extend over surprisingly large length scales.

DOI

9

Statistical mechanics of Monte Carlo sampling and the sign problem - Duering, G. and Kurchan, J.

EPL 92, (2010)

Abstract : Monte Carlo sampling of any system may be analyzed in terms of an associated glass model-a variant of the Random Energy Model-with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen and ``chaotic''), as is characteristic of glass models with complex parameters. Only the liquid one yields the correct answers for the original problem, and the task is to design the simulation to stay inside it. The statistical convergence of the sampling to the correct expectation values may be studied in these terms, yielding a general lower bound for the computer time as a function of the free energy difference between the true system, and a reference one. In this way, importance sampling strategies may be optimized. Copyright (C) EPLA, 2010

EPL 92, (2010)

LPS

Abstract : Monte Carlo sampling of any system may be analyzed in terms of an associated glass model-a variant of the Random Energy Model-with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen and ``chaotic''), as is characteristic of glass models with complex parameters. Only the liquid one yields the correct answers for the original problem, and the task is to design the simulation to stay inside it. The statistical convergence of the sampling to the correct expectation values may be studied in these terms, yielding a general lower bound for the computer time as a function of the free energy difference between the true system, and a reference one. In this way, importance sampling strategies may be optimized. Copyright (C) EPLA, 2010

DOI

10

Irreversibility and self-organization in hydrodynamic echo experiments - Duering, Gustavo and Bartolo, Denis and Kurchan, Jorge

PHYSICAL REVIEW E 79, (2009)

Abstract : We discuss the reversible-irreversible transition in low-Reynolds hydrodynamic systems driven by external cycling actuation. We introduce a set of models with no auto-organization, and show that a sharp crossover is obtained between a Lyapunov regime in which any noise source, such as thermal noise, is amplified exponentially, and a diffusive regime where this no longer holds. In the latter regime, groups of particles are seen to move cooperatively, yet no spatial organization occurs.

PHYSICAL REVIEW E 79, (2009)

LPS

Abstract : We discuss the reversible-irreversible transition in low-Reynolds hydrodynamic systems driven by external cycling actuation. We introduce a set of models with no auto-organization, and show that a sharp crossover is obtained between a Lyapunov regime in which any noise source, such as thermal noise, is amplified exponentially, and a diffusive regime where this no longer holds. In the latter regime, groups of particles are seen to move cooperatively, yet no spatial organization occurs.