901 research outputs found
Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system
We study the stationary nonequilibrium states of N point particles moving
under the influence of an electric field E among fixed obstacles (discs) in a
two dimensional torus. The total kinetic energy of the system is kept constant
through a Gaussian thermostat which produces a velocity dependent mean field
interaction between the particles. The current and the particle distribution
functions are obtained numerically and compared for small E with analytic
solutions of a Boltzmann type equation obtained by treating the collisions with
the obstacles as random independent scatterings. The agreement is surprisingly
good for both small and large N. The latter system in turn agrees with a self
consistent one particle evolution expected to hold in the limit of N going to
infinity.Comment: 14 pages, 9 figure
Heat Conduction in two-dimensional harmonic crystal with disorder
We study the problem of heat conduction in a mass-disordered two-dimensional
harmonic crystal. Using two different stochastic heat baths, we perform
simulations to determine the system size (L) dependence of the heat current
(J). For white noise heat baths we find that J ~ 1/L^a with
while correlated noise heat baths gives . A special case with
correlated disorder is studied analytically and gives a=3/2 which agrees also
with results from exact numerics.Comment: Revised version. 4 pages, 3 figure
Local Temperature and Universal Heat Conduction in FPU chains
It is shown numerically that for Fermi Pasta Ulam (FPU) chains with
alternating masses and heat baths at slightly different temperatures at the
ends, the local temperature (LT) on small scales behaves paradoxically in
steady state. This expands the long established problem of equilibration of FPU
chains. A well-behaved LT appears to be achieved for equal mass chains; the
thermal conductivity is shown to diverge with chain length N as N^(1/3),
relevant for the much debated question of the universality of one dimensional
heat conduction. The reason why earlier simulations have obtained
systematically higher exponents is explained.Comment: 4 pages, 3 figures, revised published versio
Universality of One-Dimensional Heat Conductivity
We show analytically that the heat conductivity of oscillator chains diverges
with system size N as N^{1/3}, which is the same as for one-dimensional fluids.
For long cylinders, we use the hydrodynamic equations for a crystal in one
dimension. This is appropriate for stiff systems such as nanotubes, where the
eventual crossover to a fluid only sets in at unrealistically large N. Despite
the extra equation compared to a fluid, the scaling of the heat conductivity is
unchanged. For strictly one-dimensional chains, we show that the dynamic
equations are those of a fluid at all length scales even if the static order
extends to very large N. The discrepancy between our results and numerical
simulations on Fermi-Pasta-Ulam chains is discussed.Comment: 7 pages, 2 figure
Fourier's Law: insight from a simple derivation
The onset of Fourier's law in a one-dimensional quantum system is addressed
via a simple model of weakly coupled quantum systems in contact with thermal
baths at their edges. Using analytical arguments we show that the crossover
from the ballistic (invalid Fourier's law) to diffusive (valid Fourier's law)
regimes is characterized by a thermal length-scale, which is directly related
to the profile of the local temperature. In the same vein, dephasing is shown
to give rise to a classical Fourier's law, similarly to the onset of Ohm's law
in mesoscopic conductors.Comment: 4+ pages, references and discussions adde
Thermal conductivity of the Toda lattice with conservative noise
We study the thermal conductivity of the one dimensional Toda lattice
perturbed by a stochastic dynamics preserving energy and momentum. The strength
of the stochastic noise is controlled by a parameter . We show that
heat transport is anomalous, and that the thermal conductivity diverges with
the length of the chain according to , with . In particular, the ballistic heat conduction of the
unperturbed Toda chain is destroyed. Besides, the exponent of the
divergence depends on
Reconstructing Fourier's law from disorder in quantum wires
The theory of open quantum systems is used to study the local temperature and
heat currents in metallic nanowires connected to leads at different
temperatures. We show that for ballistic wires the local temperature is almost
uniform along the wire and Fourier's law is invalid. By gradually increasing
disorder, a uniform temperature gradient ensues inside the wire and the thermal
current linearly relates to this local temperature gradient, in agreement with
Fourier's law. Finally, we demonstrate that while disorder is responsible for
the onset of Fourier's law, the non-equilibrium energy distribution function is
determined solely by the heat baths
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