70 research outputs found
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
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
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.Comment: 22 pages, 2 figures, 1 table. Typos correcte
Diagrammatics for the Inverse Problem in Spin Systems and Simple Liquids
Modeling complex systems, like neural networks, simple liquids or flocks of
birds, often works in reverse to textbook approaches: given data for which
averages and correlations are known, we try to find the parameters of a given
model consistent with it. In general, no exact calculation directly from the
model is available and we are left with expensive numerical approaches. A
particular situation is that of a perturbed Gaussian model with polynomial
corrections for continuous degrees of freedom. Indeed perturbation expansions
for this case have been implemented in the last 60 years. However, there are
models for which the exactly solvable part is non-Gaussian, such as independent
Ising spins in a field, or an ideal gas of particles. We implement a
diagrammatic perturbative scheme in weak correlations around a non-Gaussian yet
solvable probability weight. This applies in particular to spin models (Ising,
Potts, Heisenberg) with weak couplings, or to a simple liquid with a weak
interaction potential. Our method casts systems with discrete degrees of
freedom and those with continuous ones within the same theoretical framework.
When the core theory is Gaussian it reduces to the well-known Feynman
diagrammatics.Comment: 34 pages, 3 figures. Equivalent to published versio
Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
We present a general formalism for computing the largest Lyapunov exponent
and its fluctuations in spatially extended systems described by diffusive
fluctuating hydrodynamics, thus extending the concepts of dynamical system
theory to a broad range of non-equilibrium systems. Our analytical results
compare favourably with simulations of a lattice model of heat conduction. We
further show how the computation of the Lyapunov exponent for the Symmetric
Simple Exclusion Process relates to damage spreading and to a two-species pair
annihilation process, for which our formalism yields new finite size results
Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality
On the example of a mean-field Fredrickson-Andersen kinetically constrained
model, we focus on the known property that equilibrium dynamics take place at a
first-order dynamical phase transition point in the space of time-realizations.
We investigate the finite-size properties of this first order transition. By
discussing and exploiting a mapping of the classical dynamical transition -an
argued glassiness signature- to a first-order quantum transition, we show that
the quantum analogy can be exploited to extract finite-size properties, which
in many respects are similar to those in genuine mean-field quantum systems
with a first-order transition. We fully characterize the finite-size properties
of the order parameter across the first order transition
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