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J. Kurchan

Publications and source records attributed to J. Kurchan.

At least 19 recordsLinked to original sources
arXiv2015

Athermal analogue of sheared dense Brownian suspensions

The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming.

cond-mat.soft↗
arXiv2010

Scientific interview

Four leading scientists in the field of the glass transition answer to a series of questions formulated by the Editors (L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, W. van Saarloos). No specific format has been imposed to their answers: the scientists were free to answer or not to any given question, using how much space they felt appropriate. After a first round of answers, each author was given the opportunity to read the answers by his colleagues and to adjust his own answers accordingly.

cond-mat.stat-mech↗
arXiv2010

Do solids flow?

Are solids intrinsically different from liquids? Must a finite stress be applied in order to induce flow? Or, instead, do all solids only look rigid on some finite timescales and eventually flow if an infinitesimal shear stress is applied? Surprisingly, these simple questions are a matter of debate and definite answers are still lacking. Here we show that solidity is only a time-scale dependent notion: equilibrium states of matter that break spontaneously translation invariance, e.g. crystals, flow if even an infinitesimal stress is applied. However, they do so in a way inherently different from ordinary liquids since their viscosity diverges for vanishing shear stress with an essential singularity. We find an ultra-slow decrease of the shear stress as a function of the shear rate, which explains the apparent yield stress identified in rheological flow curves. Furthermore, we suggest that an alternating shear of frequency $ω$ and amplitude $γ$ should lead to a dynamic phase transition line in the ($ω$,$γ$) plane, from a 'flowing' to a 'non-flowing' phase. Finally, we apply our results to crystals, show the corresponding microscopic process leading to flow and discuss possible experimental investigations.

cond-mat.stat-mech↗
arXiv2010

Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve

We study first-order quantum phase transitions in models where the mean-field traitment is exact, and the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing.

quant-ph↗
arXiv2009

Jamming versus Glass Transitions

Recent ideas based on the properties of assemblies of frictionless particles in mechanical equilibrium provide a perspective of amorphous systems different from that offered by the traditional approach originating in liquid theory. The relation, if any, between these two points of view, and the relevance of the former to the glass phase, has been difficult to ascertain. In this paper we introduce a model for which both theories apply strictly: it exhibits on the one hand an ideal glass transition and on the other `jamming' features (fragility, soft modes) virtually identical to that of real systems. This allows us to disentangle the different contents and domains of applicability of the two physical phenomena.

cond-mat.stat-mech↗
arXiv2006

Duality and exact correlations for a model of heat conduction

We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the covariance of the energy exhibits long-range correlations in the presence of a current. We discuss the formal connection of this model with the simple symmetric exclusion process.

cond-mat.stat-mech↗
arXiv2005

Fluctuation theorem for non-equilibrium relaxational systems driven by external forces

We discuss an extension of the fluctuation theorem to stochastic models that, in the limit of zero external drive, are not able to equilibrate with their environment, extending results presented by Sellitto (cond-mat/9809186). We show that if the entropy production rate is suitably defined, its probability distribution function verifies the Fluctuation Relation with the ambient temperature replaced by a (frequency-dependent) effective temperature. We derive modified Green-Kubo relations. We illustrate these results with the simple example of an oscillator coupled to a nonequilibrium bath driven by an external force. We discuss the relevance of our results for driven glasses and the diffusion of Brownian particles in out of equilibrium media and propose a concrete experimental strategy to measure the low frequency value of the effective temperature using the fluctuations of the work done by an ac conservative field. We compare our results to related ones that appeared in the literature recently.

cond-mat.dis-nn↗
arXiv2005

Fourier law in a momentum-conserving chain

We introduce a family of Hamiltonian models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases Fourier law is verified in one dimension.

cond-mat.stat-mech↗
arXiv2003

Microscopic realizations of the Trap Model

Monte Carlo optimizations of Number Partitioning and of Diophantine approximations are microscopic realizations of `Trap Model' dynamics. This offers a fresh look at the physics behind this model, and points at other situations in which it may apply. Our results strongly suggest that in any such realization of the Trap Model, the response and correlation functions of smooth observables obey the fluctuation-dissipation theorem even in the aging regime. Our discussion for the Number Partitioning problem may be relevant for the class of optimization problems whose cost function does not scale linearly with the size, and are thus awkward from the statistical mechanic point of view.

cond-mat.stat-mech↗
arXiv2003

Putting hydrodynamic interactions to work: tagged particle separation

Separation of magnetically tagged cells is performed by attaching markers to a subset of cells in suspension and applying fields to pull from them in a variety of ways. The magnetic force is proportional to the field gradient, and the hydrodynamic interactions play only a passive, adverse role. Here we propose using a homogeneous rotating magnetic field only to make tagged particles rotate, and then performing the actual separation by means of hydrodynamic interactions, which thus play an active role. The method, which we explore here theoretically and by means of numerical simulations, lends itself naturally to sorting on large scales.

cond-mat.soft↗
arXiv2003

Dynamics and geometric properties of the k-Trigonometric model

We analyze the dynamics and the geometric properties of the Potential Energy Surfaces (PES) of the k-Trigonometric Model (kTM), defined by a fully-connected k-body interaction. This model has no thermodynamic transition for k=1, a second order one for k=2, and a first order one for k>2. In this paper we i) show that the single particle dynamics can be traced back to an effective dynamical system (with only one degree of freedom); ii) compute the diffusion constant analytically; iii) determine analytically several properties of the self correlation functions apart from the relaxation times which we calculate numerically; iv) relate the collective correlation functions to the ones of the effective degree of freedom using an exact Dyson-like equation; v) using two analytical methods, calculate the saddles of the PES that are visited by the system evolving at fixed temperature. On the one hand we minimize |grad V|^2, as usually done in the numerical study of supercooled liquids and, on the other hand, we compute the saddles with minimum distance (in configuration space) from initial equilibrium configurations. We find the same result from the two calculations and we speculate that the coincidence might go beyond the specific model investigated here.

cond-mat.stat-mech↗
arXiv2003

Tailoring symmetry groups using external alternate fields

Macroscopic systems with continuous symmetries subjected to oscillatory fields have phases and transitions that are qualitatively different from their equilibrium ones. Depending on the amplitude and frequency of the fields applied, Heisenberg ferromagnets can become XY or Ising-like -or, conversely, anisotropies can be compensated -thus changing the nature of the ordered phase and the topology of defects. The phenomena can be viewed as a dynamic form of "order by disorder".

cond-mat.stat-mech↗
arXiv2000

Edwards measures for powders and glasses

Can one construct a thermodynamics for compact, slowly moving powders and grains? A few years ago, Edwards proposed a possible step in this direction, raising the fascinating perspective that such systems have a statistical mechanics of their own, different from that of Maxwell, Boltzmann and Gibbs, allowing us to have some information while still ignoring dynamic details. Recent developments in the theory of glasses have come to confirm these ideas within mean-field. In order to go beyond, we explicitly generate Edwards' measure in a model that, although schematic, is three dimensional. Comparison of the results thus obtained with the irreversible compaction data shows very good agreement. The present framework immediately suggests new experimental checks.

cond-mat.stat-mech↗
arXiv1995

A mean-field hard-spheres model of glass

We present a model of spheres moving in a high-dimensional compact space. We relate it to a mixed matrix model with a $O(N)$ invariant model plus a $P(N)$ invariant perturbation. We then study the low pressure regime by performing a diagrammatic expansion of this matrix model. Finally, we show the results from numerical simulations and we present evidence for a glassy regime at high pressures.

cond-mat↗
arXiv1994

On the out of equilibrium order parameters in long-range spin-glases

We show that the dynamical order parameters can be reexpressed in terms of the distribution of the staggered auto-correlation and response functions. We calculate these distributions for the out of equilibrium dynamics of the Sherrington-Kirpatrick model at long times. The results suggest that the landscape this model visits at different long times in an out of equilibrium relaxation process is, in a sense, self-similar. Furthermore, there is a similarity between the landscape seen out of equilibrium at long times and the equilibrium landscape. The calculation is greatly simplified by making use of the superspace notation in the dynamical approach. This notation also highlights the rather mysterious formal connection between the dynamical and replica approaches.

cond-mat↗
arXiv1994

Matrix models as solvable glass models

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$ we obtain matrix models and for $p>2$ `tensor' models. We concentrate on the cases $p=2$ which we study analytically and numerically.

cond-mat↗
arXiv1994

Off equilibrium dynamics and aging in unfrustrated systems

We analyse the Langevin dynamics of the random walk, the scalar field, the X-Y model and the spinoidal decomposition. We study the deviations from the equilibrium dynamics theorems (FDT and homogeneity), the asymptotic behaviour of the systems and the aging phenomena. We compare the results with the dynamical behaviour of (random) spin-glass mean-field models.

cond-mat↗