1,127 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
$\sqrt{N}$ (where $N$ 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

### 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

### On the anomalous thermal conductivity of one-dimensional lattices

The divergence of the thermal conductivity in the thermodynamic limit is
thoroughly investigated. The divergence law is consistently determined with two
different numerical approaches based on equilibrium and non-equilibrium
simulations. A possible explanation in the framework of linear-response theory
is also presented, which traces back the physical origin of this anomaly to the
slow diffusion of the energy of long-wavelength Fourier modes. Finally, the
results of dynamical simulations are compared with the predictions of
mode-coupling theory.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

### Slow energy relaxation and localization in 1D lattices

We investigate the energy relaxation process produced by thermal baths at
zero temperature acting on the boundary atoms of chains of classical anharmonic
oscillators. Time-dependent perturbation theory allows us to obtain an explicit
solution of the harmonic problem: even in such a simple system nontrivial
features emerge from the interplay of the different decay rates of Fourier
modes. In particular, a crossover from an exponential to an inverse-square-root
law occurs on a time scale proportional to the system size $N$. A further
crossover back to an exponential law is observed only at much longer times (of
the order $N^3$). In the nonlinear chain, the relaxation process is initially
equivalent to the harmonic case over a wide time span, as illustrated by
simulations of the $\beta$ Fermi-Pasta-Ulam model. The distinctive feature is
that the second crossover is not observed due to the spontaneous appearance of
breathers, i.e. space-localized time-periodic solutions, that keep a finite
residual energy in the lattice. We discuss the mechanism yielding such
solutions and also explain why it crucially depends on the boundary conditions.Comment: 16 pages, 6 figure

### Fluctuation Formula in the Nose-Hoover thermostated Lorentz gas

In this paper we examine numerically the Gallavotti-Cohen fluctuation formula
for phase-space contraction rate and entropy production rate fluctuations in
the Nos\'e-Hoover thermostated periodic Lorentz gas. Our results indicate that
while the phase-space contraction rate fluctuations violate the fluctuation
formula near equilibrium states, the entropy production rate fluctuations obey
this formula near and far from equilibrium states as well.Comment: 4 pages, 8 figure

### 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

### Coupled transport in rotor models

Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.Peer reviewedPublisher PD

### Cooling nonlinear lattices toward localisation

We describe the energy relaxation process produced by surface damping on
lattices of classical anharmonic oscillators. Spontaneous emergence of
localised vibrations dramatically slows down dissipation and gives rise to
quasi-stationary states where energy is trapped in the form of a gas of weakly
interacting discrete breathers. In one dimension (1D), strong enough on--site
coupling may yield stretched--exponential relaxation which is reminiscent of
glassy dynamics. We illustrate the mechanism generating localised structures
and discuss the crucial role of the boundary conditions. For two--dimensional
(2D) lattices, the existence of a gap in the breather spectrum causes the
localisation process to become activated. A statistical analysis of the
resulting quasi-stationary state through the distribution of breathers'
energies yield information on their effective interactions.Comment: 10 pages, 11 figure

### Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

Heat conduction in three-dimensional nonlinear lattices is investigated using
a particle dynamics simulation. The system is a simple three-dimensional
extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in
which the interparticle potential has a biquadratic term together with a
harmonic term. The system size is $L\times L\times 2L$, and the heat is made to
flow in the $2L$ direction the Nose-Hoover method. Although a linear
temperature profile is realized, the ratio of enerfy flux to temperature
gradient shows logarithmic divergence with $L$. The autocorrelation function of
energy flux $C(t)$ is observed to show power-law decay as $t^{-0.98\pm 0,25}$,
which is slower than the decay in conventional momentum-cnserving
three-dimensional systems ($t^{-3/2}$). Similar behavior is also observed in
the four dimensional system.Comment: 4 pages, 5 figures. Accepted for publication in J. Phys. Soc. Japan
Letter

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