Transport Properties of a Chain of Anharmonic Oscillators with Random Flip of Velocities
Abstract
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 Tℓ and Tr and subject to constant forces τℓ and τr. If the forces differ τℓ≠τr the center of mass of the system will move of a speed Vs 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.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- December 2011
- DOI:
- 10.1007/s10955-011-0385-6
- arXiv:
- arXiv:1105.0493
- Bibcode:
- 2011JSP...145.1224B
- Keywords:
-
- Thermal conductivity;
- Green-Kubo formula;
- Non-equilibrium stationary states;
- Condensed Matter - Statistical Mechanics;
- Mathematics - Probability
- E-Print:
- Published version: J Stat Phys (2011) 145:1224-1255 DOI 10.1007/s10955-011-0385-6