341 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.
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THERMAL CONDUCTIVITY FOR A NOISY DISORDERED HARMONIC CHAIN
We consider a -dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges
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
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
Harmonic Systems With Bulk Noises
We consider a harmonic chain in contact with thermal reservoirs at different
temperatures and subject to bulk noises of different types: velocity flips or
self-consistent reservoirs. While both systems have the same covariances in the
nonequilibrium stationary state (NESS) the measures are very different. We
study hydrodynamical scaling, large deviations, fluctuations, and long range
correlations in both systems. Some of our results extend to higher dimensions
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
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
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