891 research outputs found
Entropy potential and Lyapunov exponents
According to a previous conjecture, spatial and temporal Lyapunov exponents
of chaotic extended systems can be obtained from derivatives of a suitable
function: the entropy potential. The validity and the consequences of this
hypothesis are explored in detail. The numerical investigation of a
continuous-time model provides a further confirmation to the existence of the
entropy potential. Furthermore, it is shown that the knowledge of the entropy
potential allows determining also Lyapunov spectra in general reference frames
where the time-like and space-like axes point along generic directions in the
space-time plane. Finally, the existence of an entropy potential implies that
the integrated density of positive exponents (Kolmogorov-Sinai entropy) is
independent of the chosen reference frame.Comment: 20 pages, latex, 8 figures, submitted to CHAO
A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
We study a symmetry property of momentum distribution functions in the steady
state of heat conduction. When the equation of motion is symmetric under change
of signs for all dynamical variables, the distribution function is also
symmetric. This symmetry can be broken by introduction of an asymmetric term in
the interaction potential or the on-site potential, or employing the thermal
walls as heat reservoirs. We numerically find differences of behavior of the
models with and without the on-site potential.Comment: 13 pages. submitted to JPS
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.
Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model
The recently discovered phenomenon of nonlinear supratransmission consists in
a sudden increase of the amplitude of a transmitted wave triggered by the
excitation of nonlinear localized modes of the medium. We examine this process
for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at
the other. The supratransmission regime occurs for driving frequencies above
the upper band-edge and originates from direct moving discrete breather
creation. We derive approximate analytical estimates of the supratransmission
threshold, which are in excellent agreement with numerics. When analysing the
long-time behavior, we discover that, below the supratransmission threshold, a
conducting stationary state coexists with the insulating one. We explain the
bistable nature of the energy flux in terms of the excitation of quasi-harmonic
extended waves. This leads to the analytical calculation of a
lower-transmission threshold which is also in reasonable agreement with
numerical experiments.Comment: 8 pages, 9 figures. Phys. Rev. E (accepted
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
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
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.
Scattering lengths and universality in superdiffusive L\'evy materials
We study the effects of scattering lengths on L\'evy walks in quenched
one-dimensional random and fractal quasi-lattices, with scatterers spaced
according to a long-tailed distribution. By analyzing the scaling properties of
the random-walk probability distribution, we show that the effect of the
varying scattering length can be reabsorbed in the multiplicative coefficient
of the scaling length. This leads to a superscaling behavior, where the
dynamical exponents and also the scaling functions do not depend on the value
of the scattering length. Within the scaling framework, we obtain an exact
expression for the multiplicative coefficient as a function of the scattering
length both in the annealed and in the quenched random and fractal cases. Our
analytic results are compared with numerical simulations, with excellent
agreement, and are supposed to hold also in higher dimensionsComment: 6 pages, 8 figure
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
Finite thermal conductivity in 1d lattices
We discuss the thermal conductivity of a chain of coupled rotators, showing
that it is the first example of a 1d nonlinear lattice exhibiting normal
transport properties in the absence of an on-site potential. Numerical
estimates obtained by simulating a chain in contact with two thermal baths at
different temperatures are found to be consistent with those ones based on
linear response theory. The dynamics of the Fourier modes provides direct
evidence of energy diffusion. The finiteness of the conductivity is traced back
to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis
of two variants of this model.Comment: 4 pages, 3 postscript figure
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