arXiv subjects

Frédéric Van Wijland

Publications and source records attributed to Frédéric Van Wijland.

12 recordsLinked to original sources

arXiv2019

Building a path-integral calculus: a covariant discretization approach

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path integrals have pervaded all areas of physics where fluctuation effects, quantum and/or thermal, are of paramount importance. Their appeal is based on the fact that one converts a problem formulated in terms of operators into one of sampling classical paths with a given weight. Path integrals are the mirror image of our conventional Riemann integrals, with functions replacing the real numbers one usually sums over. However, unlike conventional integrals, path integration suffers a serious drawback: in general, one cannot make non-linear changes of variables without committing an error of some sort. Thus, no path-integral based calculus is possible. Here we identify which are the deep mathematical reasons causing this important caveat, and we come up with cures for systems described by one degree of freedom. Our main result is a construction of path integration free of this longstanding problem, through a direct time-discretization procedure.

cond-mat.stat-mech↗

arXiv2018

Field-Embedded Particles Driven by Active Flips

Systems of independent active particles embedded into a fluctuating environment are relevant to many areas of soft-matter science. We use a minimal model of noninteracting spin-carrying Brownian particles in a Gaussian field and show that activity-driven spin dynamics leads to patterned order. We find that the competition between mediated interactions and active noise alone can yield such diverse behaviors as phase transitions and microphase separation, from lamellar up to hexagonal ordering of clusters of opposite magnetization. These rest on complex multibody interactions. We find regimes of stationary patterns, but also dynamical regimes of relentless birth and growth of lumps of magnetization opposite to the surrounding one. Our approach combines Monte-Carlo simulations with analytical methods based on dynamical density functional approaches.

cond-mat.soft↗

arXiv2014

Brownian dynamics: from glassy to trivial

We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the first, standard, dynamical rules lead to glassy behavior, the other one leads to a simple exponential relaxation towards equilibrium. This finding questions the intrinsic link that exists between the underlying, thermodynamical, energy landscape, and the dynamical rules with which this landscape is explored by the system. Our peculiar choice of dynam- ical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.

cond-mat.stat-mech↗

arXiv2013

Probing active forces via a fluctuation-dissipation relation: Application to living cells

We derive a new fluctuation-dissipation relation for non-equilibrium systems with long-term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be accessed. For a silica bead attached to the wall of a living cell, we identify a crossover time between thermally controlled fluctuations and those produced by the active forces. We show that the probe position is eventually slaved to the underlying random drive produced by the so-called active forces.

cond-mat.soft↗

arXiv2012

Field theoretic formulation of a mode-coupling equation for colloids

The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 80's by Götze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field theoretic formulation that arrives at very similar mode-coupling equation but which is based on a variational principle and on a controlled expansion in a small dimensioneless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions.

cond-mat.stat-mech↗

arXiv2012

Inactive dynamical phase of a symmetric exclusion process on a ring

We investigate the nature of the dynamically inactive phase of a simple symmetric exclusion process on a ring. We find that as the system's activity is tuned to a lower-than-average value the particles progressively lump into a single cluster, thereby forming a kink in the density profile. All dynamical regimes, and their finite size range of validity, are explicitly determined.

cond-mat.stat-mech↗

arXiv2011

Dynamic transition in an atomic glass former: a molecular dynamics evidence

We find that a Lennard-Jones mixture displays a dynamic phase transition between an active regime and an inactive one. By means of molecular dynamics simulations and of a finite-size study, we show that the space time dynamics in the supercooled regime coincides with a dynamic first order transition point.

cond-mat.stat-mech↗

arXiv2009

Current fluctuations in systems with diffusive dynamics, in and out of equilibrium

For diffusive systems that can be described by fluctuating hydrodynamics and by the Macroscopic Fluctuation Theory of Bertini et al., the total current fluctuations display universal features when the system is closed and in equilibrium. When the system is taken out of equilibrium by a boundary-drive, current fluctuations, at least for a particular family of diffusive systems, display the same universal features as in equilibrium. To achieve this result, we exploit a mapping between the fluctuations in a boundary-driven nonequilibrium system and those in its equilibrium counterpart. Finally, we prove, for two well-studied processes, namely the Simple Symmetric Exclusion Process and the Kipnis-Marchioro-Presutti model for heat conduction, that the distribution of the current out of equilibrium can be deduced from the distribution in equilibrium. Thus, for these two microscopic models, the mapping between the out-of-equilibrium setting and the equilibrium one is exact.

cond-mat.stat-mech↗

arXiv2009

Second-order dynamic transition in a p=2 spin-glass model

We consider the dynamics of a disordered p-spin model with p=2, analyzing the dynamics within Ruelle's thermodynamic formalism, We use an indicator of the dynamical activity to construct the relevant dynamical Gibbs ensemble. We prove that the dynamics in the low-temperature (spin glass) phase of the model take place at a second-order phase transition between dynamically active and inactive trajectories. We also show that the same behaviour is found in a related model of a three-dimensional ferromagnet.

cond-mat.dis-nn↗

arXiv2009

Equilibrium-like fluctuations in some boundary-driven open diffusive systems

There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping, for the system's fluctuations, to an equivalent open --yet equilibrium-- diffusive system. We discuss the possibility of observing dynamic phase transitions using the particle current as a control parameter.

cond-mat.stat-mech↗

arXiv2008

Slow relaxation, dynamic transitions and extreme value statistics in disordered systems

We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase transition in these models to the extreme value statistics of the associated random energy landscape.

cond-mat.stat-mech↗

arXiv2008

Universal cumulants of the current in diffusive systems on a ring

We calculate exactly the first cumulants of the integrated current and of the activity (which is the total number of changes of configurations) of the symmetric simple exclusion process (SSEP) on a ring with periodic boundary conditions. Our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form, with the same scaling function for both quantities. This scaling function can be understood either by an analysis of Bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim.

cond-mat.stat-mech↗