arXiv subjects

Stefano Lepri

Publications and source records attributed to Stefano Lepri.

79 records · Page 5Linked to original sources

arXiv1998

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.

cond-mat.stat-mech↗

arXiv1998

Lyapunov Exponents from Node-Counting Arguments

A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schrödinger problem for a particle in a disordered potential. As a consequence, we propose an alternative method to compute the Lyapunov spectrum. The implications on the foundation of the recently proposed ``chronotopic approach'' are also discussed.

chao-dyn↗

arXiv1997

Energy transport in anharmonic lattices close and far from equilibrium

The problem of stationary heat transport in the Fermi-Pasta-Ulam chain is numerically studied showing that the conductivity diverges in the thermodynamic limit. Simulations were performed with time-reversible thermostats, both for small and large temperature gradients. In the latter case, fluctuations of the heat current are shown to be in agreement with the recent conjectures of Gallavotti and Cohen.

cond-mat.stat-mech↗

arXiv1997

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.

chao-dyn↗

arXiv1996

Disturbance propagation in chaotic extended systems with long-range coupling

Propagation of initially localized perturbations is investigated in chaotic coupled map lattices with long-range couplings decaying as a power of the distance. The initial perturbation propagates exponentially fast along the lattice, with a rate given by the ratio of the maximal Lyapunov exponent and the power of the coupling. A complementary description in terms of a suitable comoving Lyapunov exponent is also given.

chao-dyn↗

arXiv1996

Chronotopic Lyapunov Analysis: (II) towards a Unified Approach

From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it gives directly the Kolmogorov-Sinai entropy density. Such a function allows determining also Lyapunov spectra in reference frames where time-like and space-like axes point in general directions in the space-time plane. The existence of an entropy potential implies that the integrated density of positive exponents is independent of the reference frame.

chao-dyn↗

arXiv1995

Chronotopic Lyapunov Analysis: (I) a Comprehensive Characterization of 1D Systems

Instabilities in 1D spatially extended systems are studied with the aid of both temporal and spatial Lyapunov exponents. A suitable representation of the spectra allows a compact description of all the possible disturbances in tangent space. The analysis is carried out for chaotic and periodic spatiotemporal patterns. Singularities of the spectra and localization properties of the associated Lyapunov vectors are discussed.

chao-dyn↗