998 research outputs found
Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
We study heat transport in a chain of harmonic oscillators with random
elastic collisions between nearest-neighbours. The equations of motion of the
covariance matrix are numerically solved for free and fixed boundary
conditions. In the thermodynamic limit, the shape of the temperature profile
and the value of the stationary heat flux depend on the choice of boundary
conditions. For free boundary conditions, they also depend on the coupling
strength with the heat baths. Moreover, we find a strong violation of local
equilibrium at the chain edges that determine two boundary layers of size
(where is the chain length), that are characterized by a
different scaling behaviour from the bulk. Finally, we investigate the
relaxation towards the stationary state, finding two long time scales: the
first corresponds to the relaxation of the hydrodynamic modes; the second is a
manifestation of the finiteness of the system.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica
The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.Comment: 12 pages, submitted to Journal of Statistical Physic
Local and average behavior in inhomogeneous superdiffusive media
We consider a random walk on one-dimensional inhomogeneous graphs built from
Cantor fractals. Our study is motivated by recent experiments that demonstrated
superdiffusion of light in complex disordered materials, thereby termed L\'evy
glasses. We introduce a geometric parameter which plays a role
analogous to the exponent characterizing the step length distribution in random
systems. We study the large-time behavior of both local and average
observables; for the latter case, we distinguish two different types of
averages, respectively over the set of all initial sites and over the
scattering sites only. The "single long jump approximation" is applied to
analytically determine the different asymptotic behaviours as a function of
and to understand their origin. We also discuss the possibility that
the root of the mean square displacement and the characteristic length of the
walker distribution may grow according to different power laws; this anomalous
behaviour is typical of processes characterized by L\'evy statistics and here,
in particular, it is shown to influence average quantities
Relaxation of classical many-body hamiltonians in one dimension
The relaxation of Fourier modes of hamiltonian chains close to equilibrium is
studied in the framework of a simple mode-coupling theory. Explicit estimates
of the dependence of relevant time scales on the energy density (or
temperature) and on the wavenumber of the initial excitation are given. They
are in agreement with previous numerical findings on the approach to
equilibrium and turn out to be also useful in the qualitative interpretation of
them. The theory is compared with molecular dynamics results in the case of the
quartic Fermi-Pasta-Ulam potential.Comment: 9 pag. 6 figs. To appear in Phys.Rev.
Asymptotic energy profile of a wavepacket in disordered chains
We investigate the long time behavior of a wavepacket initially localized at
a single site in translationally invariant harmonic and anharmonic chains
with random interactions. In the harmonic case, the energy profile averaged on time and disorder decays for large as a power
law where and 3/2 for
initial displacement and momentum excitations, respectively. The prefactor
depends on the probability distribution of the harmonic coupling constants and
diverges in the limit of weak disorder. As a consequence, the moments of the energy distribution averaged with respect to disorder
diverge in time as for , where
for . Molecular dynamics simulations yield good agreement with
these theoretical predictions. Therefore, in this system, the second moment of
the wavepacket diverges as a function of time despite the wavepacket is not
spreading. Thus, this only criteria often considered earlier as proving the
spreading of a wave packet, cannot be considered as sufficient in any model.
The anharmonic case is investigated numerically. It is found for intermediate
disorder, that the tail of the energy profile becomes very close to those of
the harmonic case. For weak and strong disorder, our results suggest that the
crossover to the harmonic behavior occurs at much larger and larger
time.Comment: To appear in Phys. Rev.
Nonequilibrium dynamics of a stochastic model of anomalous heat transport
We study the dynamics of covariances in a chain of harmonic oscillators with
conservative noise in contact with two stochastic Langevin heat baths. The
noise amounts to random collisions between nearest-neighbour oscillators that
exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math.
Theor. 42 (2009) 025001], we have studied the stationary state of this system
with fixed boundary conditions, finding analytical exact expressions for the
temperature profile and the heat current in the thermodynamic (continuum)
limit. In this paper we extend the analysis to the evolution of the covariance
matrix and to generic boundary conditions. Our main purpose is to construct a
hydrodynamic description of the relaxation to the stationary state, starting
from the exact equations governing the evolution of the correlation matrix. We
identify and adiabatically eliminate the fast variables, arriving at a
continuity equation for the temperature profile T(y,t), complemented by an
ordinary equation that accounts for the evolution in the bulk. Altogether, we
find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica
Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths
We use a Generalised Langevin Equation (GLE) scheme to study the thermal
transport of low dimensional systems. In this approach, the central classical
region is connected to two realistic thermal baths kept at two different
temperatures [H. Ness et al., Phys. Rev. B {\bf 93}, 174303 (2016)]. We
consider model Al systems, i.e. one-dimensional atomic chains connected to
three-dimensional baths. The thermal transport properties are studied as a
function of the chain length and the temperature difference
between the baths. We calculate the transport properties both in the linear
response regime and in the non-linear regime. Two different laws are obtained
for the linear conductance versus the length of the chains. For large
temperatures ( K) and temperature differences ( K), the chains, with atoms, present a diffusive transport regime
with the presence of a temperature gradient across the system. For lower
temperatures( K) and temperature differences ( K), a regime similar to the ballistic regime is observed. Such a
ballistic-like regime is also obtained for shorter chains (). Our
detailed analysis suggests that the behaviour at higher temperatures and
temperature differences is mainly due to anharmonic effects within the long
chains.Comment: Accepted for publication in J. Chem. Phy
Anomalous kinetics and transport from 1D self--consistent mode--coupling theory
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D)
many-particle systems as described by self-consistent mode-coupling theory. The
corresponding nonlinear integro-differential equations for the relevant
correlators are solved analytically and checked numerically. In particular, we
find that the memory functions exhibit a power-law decay accompanied by
relatively fast oscillations. Furthermore, the scaling behaviour and,
correspondingly, the universality class depends on the order of the leading
nonlinear term. In the cubic case, both viscosity and thermal conductivity
diverge in the thermodynamic limit. In the quartic case, a faster decay of the
memory functions leads to a finite viscosity, while thermal conductivity
exhibits an even faster divergence. Finally, our analysis puts on a more firm
basis the previously conjectured connection between anomalous heat conductivity
and anomalous diffusion
A simple one-dimensional model of heat conduction which obeys Fourier's law
We present the computer simulation results of a chain of hard point particles
with alternating masses interacting on its extremes with two thermal baths at
different temperatures. We found that the system obeys Fourier's law at the
thermodynamic limit. This result is against the actual belief that one
dimensional systems with momentum conservative dynamics and nonzero pressure
have infinite thermal conductivity. It seems that thermal resistivity occurs in
our system due to a cooperative behavior in which light particles tend to
absorb much more energy than the heavier ones.Comment: 5 pages, 4 figures, to be published in PR
Energy diffusion in hard-point systems
We investigate the diffusive properties of energy fluctuations in a
one-dimensional diatomic chain of hard-point particles interacting through a
square--well potential. The evolution of initially localized infinitesimal and
finite perturbations is numerically investigated for different density values.
All cases belong to the same universality class which can be also interpreted
as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit
is nevertheless exceptional in that normal diffusion is found in tangent space
and yet anomalous diffusion with a different rate for perturbations of finite
amplitude. The different behaviour of the two classes of perturbations is
traced back to the "stable chaos" type of dynamics exhibited by this model.
Finally, the effect of an additional internal degree of freedom is
investigated, finding that it does not modify the overall scenarioComment: 16 pages, 15 figure
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