3,306 research outputs found
Exact dynamics in dual-unitary quantum circuits
We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs
Long range correlations and phase transition in non-equilibrium diffusive systems
We obtain explicit expressions for the long range correlations in the ABC
model and in diffusive models conditioned to produce an atypical current of
particles.In both cases, the two-point correlation functions allow to detect
the occurrence of a phase transition as they become singular when the system
approaches the transition
Vortices in the two-dimensional Simple Exclusion Process
We show that the fluctuations of the partial current in two dimensional
diffusive systems are dominated by vortices leading to a different scaling from
the one predicted by the hydrodynamic large deviation theory. This is supported
by exact computations of the variance of partial current fluctuations for the
symmetric simple exclusion process on general graphs. On a two-dimensional
torus, our exact expressions are compared to the results of numerical
simulations. They confirm the logarithmic dependence on the system size of the
fluctuations of the partialflux. The impact of the vortices on the validity of
the fluctuation relation for partial currents is also discussed.Comment: Revised version to appear in Journal of Statistical Physics. Minor
correction
Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution
The probability distribution of the current in the asymmetric simple
exclusion process is expected to undergo a phase transition in the regime of
weak asymmetry of the jumping rates. This transition was first predicted by
Bodineau and Derrida using a linear stability analysis of the hydrodynamical
limit of the process and further arguments have been given by Mallick and
Prolhac. However it has been impossible so far to study what happens after the
transition. The present paper presents an analysis of the large deviation
function of the current on both sides of the transition from a Bethe ansatz
approach of the weak asymmetry regime of the exclusion process.Comment: accepted to J.Stat.Phys, 1 figure, 1 reference, 2 paragraphs adde
A diffusive system driven by a battery or by a smoothly varying field
We consider the steady state of a one dimensional diffusive system, such as
the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at
the origin or by a smoothly varying field along the ring. The battery appears
as the limiting case of a smoothly varying field, when the field becomes a
delta function at the origin. We find that in the scaling limit, the long range
pair correlation functions of the system driven by a battery turn out to be
very different from the ones known in the steady state of the SSEP maintained
out of equilibrium by contact with two reservoirs, even when the steady state
density profiles are identical in both models
Non equilibrium current fluctuations in stochastic lattice gases
We study current fluctuations in lattice gases in the macroscopic limit
extending the dynamic approach for density fluctuations developed in previous
articles. More precisely, we establish a large deviation principle for a
space-time fluctuation of the empirical current with a rate functional \mc
I (j). We then estimate the probability of a fluctuation of the average
current over a large time interval; this probability can be obtained by solving
a variational problem for the functional \mc I . We discuss several possible
scenarios, interpreted as dynamical phase transitions, for this variational
problem. They actually occur in specific models. We finally discuss the time
reversal properties of \mc I and derive a fluctuation relationship akin to
the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur
Crossover to the KPZ equation
We characterize the crossover regime to the KPZ equation for a class of
one-dimensional weakly asymmetric exclusion processes. The crossover depends on
the strength asymmetry () and it occurs at
. We show that the density field is a solution of an
Ornstein-Uhlenbeck equation if , while for it is
an energy solution of the KPZ equation. The corresponding crossover for the
current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012),
813-82
A nonequilibrium extension of the Clausius heat theorem
We generalize the Clausius (in)equality to overdamped mesoscopic and
macroscopic diffusions in the presence of nonconservative forces. In contrast
to previous frameworks, we use a decomposition scheme for heat which is based
on an exact variant of the Minimum Entropy Production Principle as obtained
from dynamical fluctuation theory. This new extended heat theorem holds true
for arbitrary driving and does not require assumptions of local or close to
equilibrium. The argument remains exactly intact for diffusing fields where the
fields correspond to macroscopic profiles of interacting particles under
hydrodynamic fluctuations. We also show that the change of Shannon entropy is
related to the antisymmetric part under a modified time-reversal of the
time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende
Dynamics and Lax-Phillips scattering for generalized Lamb models
This paper treats the dynamics and scattering of a model of coupled
oscillating systems, a finite dimensional one and a wave field on the half
line. The coupling is realized producing the family of selfadjoint extensions
of the suitably restricted self-adjoint operator describing the uncoupled
dynamics. The spectral theory of the family is studied and the associated
quadratic forms constructed. The dynamics turns out to be Hamiltonian and the
Hamiltonian is described, including the case in which the finite dimensional
systems comprises nonlinear oscillators; in this case the dynamics is shown to
exist as well. In the linear case the system is equivalent, on a dense
subspace, to a wave equation on the half line with higher order boundary
conditions, described by a differential polynomial explicitely
related to the model parameters. In terms of such structure the Lax-Phillips
scattering of the system is studied. In particular we determine the incoming
and outgoing translation representations, the scattering operator, which turns
out to be unitarily equivalent to the multiplication operator given by the
rational function , and the Lax-Phillips semigroup,
which describes the evolution of the states which are neither incoming in the
past nor outgoing in the future
Current reservoirs in the simple exclusion process
We consider the symmetric simple exclusion process in the interval
with additional birth and death processes respectively on , , and
. The exclusion is speeded up by a factor , births and deaths
by a factor . Assuming propagation of chaos (a property proved in a
companion paper "Truncated correlations in the stirring process with births and
deaths") we prove convergence in the limit to the linear heat
equation with Dirichlet condition on the boundaries; the boundary conditions
however are not known a priori, they are obtained by solving a non linear
equation. The model simulates mass transport with current reservoirs at the
boundaries and the Fourier law is proved to hold
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