Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises
  We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ 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. 
Cedric Bernardin (UMPA-ENSL), Venkateshan Kannan, Joel L. Lebowitz,   Jani Lukkarinen
cond-mat.stat-mech math.PR