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13 results on '"Thibaud Maimbourg"'

1. Density scaling of generalized Lennard-Jones fluids in different dimensions

Author

Thibaud Maimbourg, Jeppe C. Dyre, Lorenzo Costigliola

Subjects
Physics, QC1-999
Abstract

Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. These scaling properties do not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, the comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.

Published
2020
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2. Generating dense packings of hard spheres by soft interaction design

Author

Thibaud Maimbourg, Mauro Sellitto, Guilhem Semerjian, Francesco Zamponi

Subjects
Physics, QC1-999
Abstract

Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7\, d\, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.

Published
2018
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3. Impact of jamming criticality on low-temperature anomalies in structural glasses

Author

Silvio Franz, Giorgio Parisi, Thibaud Maimbourg, Antonello Scardicchio, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Abdus Salam International Centre for Theoretical Physics [Trieste] (ICTP), Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica, and Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome]

Subjects
Physics, [PHYS]Physics [physics], Multidisciplinary, Condensed matter physics, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Jamming, Disordered Systems and Neural Networks (cond-mat.dis-nn), Renormalization group, Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, 010305 fluids & plasmas, symbols.namesake, Critical point (thermodynamics), Physical Sciences, 0103 physical sciences, symbols, 010306 general physics, Scaling, Debye model, Condensed Matter - Statistical Mechanics, Marginal stability, Phase diagram, Debye
Abstract

We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling (ii) The vicinity of the classical jamming critical point, as the crossover temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold., Comment: 7 pages + 38 pages SI, 5 figures

Published
2019
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4. Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain

Author

Thibaud Maimbourg, Francesco Zamponi, Elisabeth Agoritsas, Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, out-of-equilibrium dynamics-mean field, FOS: Physical sciences, metastable glassy states, General Physics and Astronomy, 01 natural sciences, 010305 fluids & plasmas, disordered systems, metastable states, 0103 physical sciences, Shear stress, 010306 general physics, Anisotropy, Langevin dynamics, Mathematical Physics, Condensed Matter - Statistical Mechanics, glass, [PHYS]Physics [physics], Physics, Particle system, Statistical Mechanics (cond-mat.stat-mech), Stochastic process, Isotropy, Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, scenario, Condensed Matter::Soft Condensed Matter, Classical mechanics, Modeling and Simulation, rheology, Restoring force, Equations for a falling body, hard-sphere fluid
Abstract

As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in $d$ dimensions, submitted to an external shear strain. We show that the anisotropy introduced by the shear strain can be simply addressed by moving into the co-shearing frame, leading to simple dynamical mean field equations in the limit ${d\to\infty}$. The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels - self-consistently determined by the process itself - encoding the effective restoring force, friction and noise terms due to the particle interactions. From there one can compute dynamical observables such as particle mean-square displacements and shear stress fluctuations, and eventually aim at providing an exact ${d \to \infty}$ benchmark for liquid and glass rheology. As an application of our results, we derive dynamically the 'state-following' equations that describe the static response of a glass to a finite shear strain until it yields., Typo corrected in Eq. (47)

Published
2019
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5. Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case

Author

Thibaud Maimbourg, Francesco Zamponi, Elisabeth Agoritsas, Ecole Polytechnique Fédérale de Lausanne (EPFL), Abdus Salam International Centre for Theoretical Physics [Trieste] (ICTP), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)

Subjects
Statistics and Probability, mean field, liquids, FOS: Physical sciences, General Physics and Astronomy, metastable glassy states, 01 natural sciences, 010305 fluids & plasmas, nonequilibrium dynamics, disordered systems, 0103 physical sciences, metastable states, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Langevin dynamics, ComputingMilieux_MISCELLANEOUS, Mathematical Physics, Condensed Matter - Statistical Mechanics, Physics, Particle system, mode-coupling theory, Statistical Mechanics (cond-mat.stat-mech), Isotropy, mean-field theory, Statistical and Nonlinear Physics, Observable, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, connections, Condensed Matter::Soft Condensed Matter, Classical mechanics, Mean field theory, Modeling and Simulation, out-of-equilibrium dynamics, lennard-jones mixture, structural glass-transition, Particle, rheology, Equations for a falling body, Quasistatic process, hard-sphere fluid
Abstract

We consider the Langevin dynamics of a many-body system of interacting particles in $d$ dimensions, in a very general setting suitable to model several out-of-equilibrium situations, such as liquid and glass rheology, active self-propelled particles, and glassy aging dynamics. The pair interaction potential is generic, and can be chosen to model colloids, atomic liquids, and granular materials. In the limit ${d\to\infty}$, we show that the dynamics can be exactly reduced to a single one-dimensional effective stochastic equation, with an effective thermal bath described by kernels that have to be determined self-consistently. We present two complementary derivations, via a dynamical cavity method and via a path-integral approach. From the effective stochastic equation, one can compute dynamical observables such as pressure, shear stress, particle mean-square displacement, and the associated response function. As an application of our results, we derive dynamically the `state-following' equations that describe the response of a glass to quasistatic perturbations, thus bypassing the use of replicas. The article is written in a modular way, that allows the reader to skip the details of the derivations and focus on the physical setting and the main results.

Published
2018
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6. Generating dense packings of hard spheres by soft interaction design

Author

Mauro Sellitto, Guilhem Semerjian, Francesco Zamponi, Thibaud Maimbourg, Maimbourg, Thibaud, Sellitto, Mauro, Semerjian, Guilhem, Zamponi, Francesco, Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)

Subjects
Dimension (graph theory), FOS: Physical sciences, General Physics and Astronomy, Condensed Matter - Soft Condensed Matter, Atomic packing factor, 01 natural sciences, Upper and lower bounds, 010305 fluids & plasmas, 0103 physical sciences, Statistical physics, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, [PHYS]Physics [physics], Physics, Statistical Mechanics (cond-mat.stat-mech), Isotropy, Order (ring theory), Disordered Systems and Neural Networks (cond-mat.dis-nn), Hard spheres, Condensed Matter - Disordered Systems and Neural Networks, lcsh:QC1-999, Sphere packing, Soft Condensed Matter (cond-mat.soft), SPHERES, lcsh:Physics
Abstract

Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7\, d\, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension., Comment: 28 pages, 5 figures, 2 tables. Submission to SciPost. Added clarifications and references

Published
2018
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7. Approximate scale invariance in particle systems: a large-dimensional justification

Author

Jorge Kurchan, Thibaud Maimbourg, Laboratoire de Physique Théorique de l'ENS (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Statistique de l'ENS (LPS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Particle system, Physics, PACS 05.20.-y – Classical statistical mechanicsPACS 64.70.pm – LiquidsPACS 89.75.Da – Systems obeying scaling laws, Class (set theory), Statistical Mechanics (cond-mat.stat-mech), 010304 chemical physics, Series (mathematics), Exponential potential, FOS: Physical sciences, General Physics and Astronomy, Disordered Systems and Neural Networks (cond-mat.dis-nn), Scale invariance, Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, 0103 physical sciences, Limit (mathematics), Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Condensed Matter - Statistical Mechanics
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., 11 pages, 3 figures -- New version includes added discussions, figures and references, as well as an appendix about the derivation of equations

Published
2016
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8. Solution of the Dynamics of Liquids in the Large-Dimensional Limit

Author

Jorge Kurchan, Francesco Zamponi, and Thibaud Maimbourg

Subjects
Physics, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, General Physics and Astronomy, Spherical coordinate system, Disordered Systems and Neural Networks (cond-mat.dis-nn), 02 engineering and technology, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter, 021001 nanoscience & nanotechnology, 01 natural sciences, Upper and lower bounds, Classical mechanics, Colors of noise, 0103 physical sciences, Virial expansion, Soft Condensed Matter (cond-mat.soft), Limit (mathematics), Statistical physics, Diffusion (business), 010306 general physics, 0210 nano-technology, Glass transition, Condensed Matter - Statistical Mechanics, Saddle
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., Comment: 4 pages + Appendix with 25 pages and 5 figures

Published
2016
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9. Statics and dynamics of infinite-dimensional liquids and glasses: a parallel and compact derivation

Author

Francesco Zamponi, Jorge Kurchan, Thibaud Maimbourg, Laboratoire de Physique Statistique de l'ENS (LPS), Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Physics, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, 010305 fluids & plasmas, Classical mechanics, 0103 physical sciences, Soft Condensed Matter (cond-mat.soft), [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Statistics, Probability and Uncertainty, 010306 general physics, [PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft], Statics, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS
Abstract

We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the replica method. The dynamic derivation is based on the general analogy between replicas and the supersymmetric formulation of dynamics. We show that static and dynamic results are consistent, and follow the Random First Order Transition scenario of mean field disordered glassy systems., 49 pages, 2 figures

Published
2016
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10. Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain.

Author

Elisabeth Agoritsas, Thibaud Maimbourg, and Francesco Zamponi

Subjects
*SHEAR strain, *SHEARING force, *PARTICLE interactions, *EQUATIONS, *STOCHASTIC processes
Abstract

As an extension of the isotropic setting presented in the companion paper Agoritsas et al (2019 J. Phys. A: Math. Theor. 52 144002), we consider the Langevin dynamics of a many-body system of pairwise interacting particles in d dimensions, submitted to an external shear strain. We show that the anisotropy introduced by the shear strain can be simply addressed by moving into the co-shearing frame, leading to simple dynamical mean field equations in the limit . The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels—self-consistently determined by the process itself—encoding the effective restoring force, friction and noise terms due to the particle interactions. From there one can compute dynamical observables such as particle mean-square displacements and shear stress fluctuations, and eventually aim at providing an exact benchmark for liquid and glass rheology. As an application of our results, we derive dynamically the ‘state-following’ equations that describe the static response of a glass to a finite shear strain until it yields. [ABSTRACT FROM AUTHOR]

Published
2019
Full Text
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11. Out-of-equilibrium dynamical equations of infinite-dimensional particle systems I. The isotropic case.

Author

Elisabeth Agoritsas, Thibaud Maimbourg, and Francesco Zamponi

Subjects
*GRANULAR materials, *COLLOIDS, *EQUATIONS
Abstract

We consider the Langevin dynamics of a many-body system of interacting particles in d dimensions, in a very general setting suitable to model several out-of-equilibrium situations, such as liquid and glass rheology, active self-propelled particles, and glassy aging dynamics. The pair interaction potential is generic, and can be chosen to model colloids, atomic liquids, and granular materials. In the limit , we show that the dynamics can be exactly reduced to a single one-dimensional effective stochastic equation, with an effective thermal bath described by kernels that have to be determined self-consistently. We present two complementary derivations, via a dynamical cavity method and via a path-integral approach. From the effective stochastic equation, one can compute dynamical observables such as pressure, shear stress, particle mean-square displacement, and the associated response function. As an application of our results, we derive dynamically the ‘state-following’ equations that describe the response of a glass to quasistatic perturbations, thus bypassing the use of replicas. The article is written in a modular way, that allows the reader to skip the details of the derivations and focus on the physical setting and the main results. [ABSTRACT FROM AUTHOR]

Published
2019
Full Text
View/download PDF

12. Approximate scale invariance in particle systems: A large-dimensional justification.

Author

Thibaud Maimbourg and Jorge Kurchan

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. [ABSTRACT FROM AUTHOR]

Published
2016
Full Text
View/download PDF

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