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Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities

Olla, Stefano; Bernardin, Cédric (2011), Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities, Journal of Statistical Physics, 145, 5, p. 1224-1255. http://dx.doi.org/10.1007/s10955-011-0385-6

Type
Article accepté pour publication ou publié
External document link
http://hal-ens-lyon.archives-ouvertes.fr/ensl-00589672/fr/
Date
2011
Journal name
Journal of Statistical Physics
Volume
145
Number
5
Publisher
Springer
Pages
1224-1255
Publication identifier
http://dx.doi.org/10.1007/s10955-011-0385-6
Metadata
Show full item record
Author(s)
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Bernardin, Cédric
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Abstract (EN)
We consider the stationary states of a chain of $n$ anharmonic coupled oscillators, whose deterministic hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature $T_\ell$ and $T_r$ and subject to constant forces $\tau_\ell$ and $\tau_r$. If the forces differ $\tau_\ell \neq \tau_r$ the center of mass of the system will move of a speed $V_s$ inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity. We investigate the entropy production properties of the stationary states, and we prove the existence of the Onsager matrix defined by Green-kubo formulas (linear response). We also prove some explicit bounds on the thermal conductivity, depending on the temperature.
Subjects / Keywords
non-equilibrium stationary states; Green-Kubo formula; Thermal conductivity

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