Eur. Phys. J. B 84, 685-689 (2011)
https://doi.org/10.1140/epjb/e2011-20746-0

Regular Article

Nonequilibrium stationary states of harmonic chains with bulk noises

¹ Universitéde Lyon and CNRS, UMPA, UMR-CNRS 5669, ENS-Lyon, 46, allée d’Italie, 69364 Lyon Cedex 07, France
² Department of Mathematics and Physics, Rutgers University, Piscataway, NJ, USA
³ Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsingin Yliopisto, Finland

^a e-mail: cedric.bernardin@ens-lyon.fr

Received: 8 September 2011
Published online: 21 November 2011

Abstract

We consider a chain composed of N coupled harmonic oscillators in contact with heat baths at temperature T_ℓ and T_r at sites 1 and N respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier’s law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.