370 research outputs found
Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities
We consider the stationary states of a chain of anharmonic coupled
oscillators, whose deterministic hamiltonian dynamics is perturbed by random
independent sign change of the velocities (a random mechanism that conserve
energy). The extremities are coupled to thermostats at different temperature
and and subject to constant forces and . If
the forces differ the center of mass of the system will
move of a speed inducing a tension gradient inside the system. Our aim is
to see the influence of the tension gradient on the thermal conductivity. We
investigate the entropy production properties of the stationary states, and we
prove the existence of the Onsager matrix defined by Green-kubo formulas
(linear response). We also prove some explicit bounds on the thermal
conductivity, depending on the temperature.Comment: Published version: J Stat Phys (2011) 145:1224-1255 DOI
10.1007/s10955-011-0385-
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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.
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
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
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
A momentum conserving model with anomalous thermal conductivity in low dimension
Anomalous large thermal conductivity has been observed numerically and
experimentally in one and two dimensional systems. All explicitly solvable
microscopic models proposed to date did not explain this phenomenon and there
is an open debate about the role of conservation of momentum. We introduce a
model whose thermal conductivity diverges in dimension 1 and 2 if momentum is
conserved, while it remains finite in dimension . We consider a system
of harmonic oscillators perturbed by a non-linear stochastic dynamics
conserving momentum and energy. We compute explicitly the time correlation
function of the energy current , and we find that it behaves, for
large time, like in the unpinned cases, and like when
an on site harmonic potential is present. Consequently thermal conductivity is
finite if or if an on-site potential is present, while it is infinite
in the other cases. This result clarifies the role of conservation of momentum
in the anomalous thermal conductivity in low dimensions
Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
We study the thermal conductivity, at fixed positive temperature, of a
disordered lattice of harmonic oscillators, weakly coupled to each other
through anharmonic potentials. The interaction is controlled by a small
parameter . We rigorously show, in two slightly different setups,
that the conductivity has a non-perturbative origin. This means that it decays
to zero faster than any polynomial in as . It
is then argued that this result extends to a disordered chain studied by Dhar
and Lebowitz, and to a classical spins chain recently investigated by
Oganesyan, Pal and Huse.Comment: 21 page
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
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