Perturbative analysis of anharmonic chains of oscillators out of equilibrium

Abstract

We compute the first-order correction to the correlation functions of the stationary state of a stochastically forced harmonic chain out of equilibrium when a small on-site anharmonic potential is added. This is achieved by deriving a suitable formula for the covariance matrix of the invariant state. We find that the first-order correction of the heat current does not depend on the size of the system. Second, the temperature profile is linear when the harmonic part of the on-site potential is zero. The sign of the gradient of the profile, however, is opposite to the sign of the temperature difference of the two heat baths.

arXiv comment26 pages, 2 figures, corrected typos

References in corpus (8)

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Cited by in corpus (3)

• The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
• Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs
• Energy Dissipation in Hamiltonian Chains of Rotators