We analyze the non-equilibrium steady states (NESS) of a one dimensional harmonic chain of N atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile defined through the local kinetic energy T (j) ≡ < p 2 j >/m j , oscillates with period two in the bulk of the system. Depending on boundary conditions, either the heavier or the lighter particles in the bulk are hotter. We obtain exact expressions for the bulk temperature profile and steady state current in the limit N → ∞. These depend on whether N is odd or even.We also study similar temperature oscillations in the NESS of systems with noise in the dynamics.These die out as N → ∞.
We consider a harmonic chain in contact with thermal reservoirs at different temperatures and subject to bulk noises of different types: velocity flips or self-consistent reservoirs. While both systems have the same covariances in the non-equilibrium stationary state (NESS) the measures are very different. We study hydrodynamical scaling, large deviations, fluctuations, and long range correlations in both systems. Some of our results extend to higher dimensions.
Abstract. We consider a chain composed of N coupled harmonic oscillators in contact with heat baths at temperature T ℓ and Tr 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.
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