362 research outputs found
Thermal conductivity in harmonic lattices with random collisions
We review recent rigorous mathematical results about the macroscopic
behaviour of harmonic chains with the dynamics perturbed by a random exchange
of velocities between nearest neighbor particles. The random exchange models
the effects of nonlinearities of anharmonic chains and the resulting dynamics
have similar macroscopic behaviour. In particular there is a superdiffusion of
energy for unpinned acoustic chains. The corresponding evolution of the
temperature profile is governed by a fractional heat equation. In non-acoustic
chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics
volume "Thermal transport in low dimensions: from statistical physics to
nanoscale heat transfer" (S. Lepri ed.
Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained.FCTEgid
Anomalous diffusion for a class of systems with two conserved quantities
We introduce a class of one dimensional deterministic models of energy-volume
conserving interfaces. Numerical simulations show that these dynamics are
genuinely super-diffusive. We then modify the dynamics by adding a conservative
stochastic noise so that it becomes ergodic. System of conservation laws are
derived as hydrodynamic limits of the modified dynamics. Numerical evidence
shows these models are still super-diffusive. This is proven rigorously for
harmonic potentials
From normal diffusion to superdiffusion of energy in the evanescent flip noise limit
Published online: 18 March 2015We consider a harmonic chain perturbed by an energy conserving noise depending on a parameter . When is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when , the energy superdiffuses according to a fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of
Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise
We review some recent results on the anomalous diffusion of energy in systems
of 1D coupled oscillators and we revisit the role of momentum conservation.Comment: Proceedings of the conference PSPDE 2012
https://sites.google.com/site/meetingpspde
Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the dynamical large deviations for a particle system in which
particles may have different velocities. We assume that we have two infinite
reservoirs of particles at the boundary: this is the so-called boundary driven
process. The dynamics we considered consists of a weakly asymmetric simple
exclusion process with collision among particles having different velocities
Asymptotics of the solutions of the stochastic lattice wave equation
We consider the long time limit theorems for the solutions of a discrete wave
equation with a weak stochastic forcing. The multiplicative noise conserves the
energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck
equation for the limit wave function that holds both for square integrable and
statistically homogeneous initial data. The limit is understood in the
point-wise sense in the former case, and in the weak sense in the latter. On
the other hand, the weak limit for square integrable initial data is
deterministic
On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics
We present a lattice gas model that without fine tuning of parameters is
expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ)
universality class. To this end, we review briefly how non-linear fluctuating
hydrodynamics in one dimension predicts that all dynamical universality classes
in its range of applicability belong to an infinite discrete family which we
call Fibonacci family since their dynamical exponents are the Kepler ratios
of neighbouring Fibonacci numbers , including
diffusion (), KPZ (), and the limiting ratio which is the
golden mean . Then we revisit the case of two
conservation laws to which the modified KPZ model belongs. We also derive
criteria on the macroscopic currents to lead to other non-KPZ universality
classes.Comment: 17 page
Thermal Conductivity for a Momentum Conserving Model
We introduce a model whose thermal conductivity diverges in dimension 1 and
2, while it remains finite in dimension 3. We consider a system of oscillators
perturbed by a stochastic dynamics conserving momentum and energy. We compute
thermal conductivity via Green-Kubo formula. In the harmonic case we compute
the current-current time correlation function, that decay like in
the unpinned case and like if a on-site harmonic potential is
present. This implies a finite conductivity in or in pinned cases, and
we compute it explicitly. For general anharmonic strictly convex interactions
we prove some upper bounds for the conductivity that behave qualitatively as in
the harmonic cases.Comment: Accepted for the publication in Communications in Mathematical
Physic
Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
The continuum Kardar-Parisi-Zhang equation in one dimension is lattice
discretized in such a way that the drift part is divergence free. This allows
to determine explicitly the stationary measures. We map the lattice KPZ
equation to a bosonic field theory which has a cubic anti-hermitian
nonlinearity. Thereby it is established that the stationary two-point function
spreads superdiffusively.Comment: 21 page
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