106 research outputs found
On the structure of correlations in the three dimensional spin glasses
We investigate the low temperature phase of three-dimensional
Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed
value of the overlap the model fulfills the clustering property: the
connected correlation functions between two local overlaps decay as a power
whose exponent is independent of for all . Our findings
are in agreement with the RSB theory and show that the overlap is a good order
parameter.Comment: 5 pages, 5 figure
Interaction Flip Identities for non Centered Spin Glasses
We consider spin glass models with non-centered interactions and investigate
the effect, on the random free energies, of flipping the interaction in a
subregion of the entire volume. A fluctuation bound obtained by martingale
methods produces, with the help of integration by parts technique, a family of
polynomial identities involving overlaps and magnetizations
Duality in interacting particle systems and boson representation
In the context of Markov processes, we show a new scheme to derive dual
processes and a duality function based on a boson representation. This scheme
is applicable to a case in which a generator is expressed by boson creation and
annihilation operators. For some stochastic processes, duality relations have
been known, which connect continuous time Markov processes with discrete state
space and those with continuous state space. We clarify that using a generating
function approach and the Doi-Peliti method, a birth-death process (or discrete
random walk model) is naturally connected to a differential equation with
continuous variables, which would be interpreted as a dual Markov process. The
key point in the derivation is to use bosonic coherent states as a bra state,
instead of a conventional projection state. As examples, we apply the scheme to
a simple birth-coagulation process and a Brownian momentum process. The
generator of the Brownian momentum process is written by elements of the
SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same
scheme is available.Comment: 13 page
Conservative interacting particles system with anomalous rate of ergodicity
We analyze certain conservative interacting particle system and establish
ergodicity of the system for a family of invariant measures. Furthermore, we
show that convergence rate to equilibrium is exponential. This result is of
interest because it presents counterexample to the standard assumption of
physicists that conservative system implies polynomial rate of convergence.Comment: 16 pages; In the previous version there was a mistake in the proof of
uniqueness of weak Leray solution. Uniqueness had been claimed in a space of
solutions which was too large (see remark 2.6 for more details). Now the
mistake is corrected by introducing a new class of moderate solutions (see
definition 2.10) where we have both existence and uniquenes
Can translation invariant systems exhibit a Many-Body Localized phase?
This note is based on a talk by one of us, F. H., at the conference PSPDE II,
Minho 2013. We review some of our recent works related to (the possibility of)
Many-Body Localization in the absence of quenched disorder (in particular
arXiv:1305.5127,arXiv:1308.6263,arXiv:1405.3279). In these works, we provide
arguments why systems without quenched disorder can exhibit `asymptotic'
localization, but not genuine localization.Comment: To appear in the Proceedings of the conference Particle systems and
PDE's - II, held at the Center of Mathematics of the University of Minho in
December 201
Nonequilibrium Microscopic Distribution of Thermal Current in Particle Systems
A nonequilibrium distribution function of microscopic thermal current is
studied by a direct numerical simulation in a thermal conducting steady state
of particle systems. Two characteristic temperatures of the thermal current are
investigated on the basis of the distribution. It is confirmed that the
temperature depends on the current direction; Parallel temperature to the
heat-flux is higher than antiparallel one. The difference between the parallel
temperature and the antiparallel one is proportional to a macroscopic
temperature gradient.Comment: 4 page
On the universality of anomalous one-dimensional heat conductivity
In one and two dimensions, transport coefficients may diverge in the
thermodynamic limit due to long--time correlation of the corresponding
currents. The effective asymptotic behaviour is addressed with reference to the
problem of heat transport in 1d crystals, modeled by chains of classical
nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium
numerical simulations confirm that the finite-size thermal conductivity
diverges with the system size as . However, the
exponent deviates systematically from the theoretical prediction
proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev.
Lett. {\bf 89}, 200601 (2002)].Comment: 4 pages, submitted to Phys.Rev.
Hamiltonian dynamics of the two-dimensional lattice phi^4 model
The Hamiltonian dynamics of the classical model on a two-dimensional
square lattice is investigated by means of numerical simulations. The
macroscopic observables are computed as time averages. The results clearly
reveal the presence of the continuous phase transition at a finite energy
density and are consistent both qualitatively and quantitatively with the
predictions of equilibrium statistical mechanics. The Hamiltonian microscopic
dynamics also exhibits critical slowing down close to the transition. Moreover,
the relationship between chaos and the phase transition is considered, and
interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure
Finite thermal conductivity in 1d lattices
We discuss the thermal conductivity of a chain of coupled rotators, showing
that it is the first example of a 1d nonlinear lattice exhibiting normal
transport properties in the absence of an on-site potential. Numerical
estimates obtained by simulating a chain in contact with two thermal baths at
different temperatures are found to be consistent with those ones based on
linear response theory. The dynamics of the Fourier modes provides direct
evidence of energy diffusion. The finiteness of the conductivity is traced back
to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis
of two variants of this model.Comment: 4 pages, 3 postscript figure
Stochastic interacting particle systems out of equilibrium
This paper provides an introduction to some stochastic models of lattice
gases out of equilibrium and a discussion of results of various kinds obtained
in recent years. Although these models are different in their microscopic
features, a unified picture is emerging at the macroscopic level, applicable,
in our view, to real phenomena where diffusion is the dominating physical
mechanism. We rely mainly on an approach developed by the authors based on the
study of dynamical large fluctuations in stationary states of open systems. The
outcome of this approach is a theory connecting the non equilibrium
thermodynamics to the transport coefficients via a variational principle. This
leads ultimately to a functional derivative equation of Hamilton-Jacobi type
for the non equilibrium free energy in which local thermodynamic variables are
the independent arguments. In the first part of the paper we give a detailed
introduction to the microscopic dynamics considered, while the second part,
devoted to the macroscopic properties, illustrates many consequences of the
Hamilton-Jacobi equation. In both parts several novelties are included.Comment: 36 page
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