Non-equilibrium stationary state of a harmonic crystal with alternating masses

Details Non-equilibrium stationary state of a harmonic crystal with alternating masses Non-equilibrium stationary state of a harmonic crystal with alternating masses

2011-12-27

arxiv.org/abs/1112.5918v2

Physics

Mathematical Physics

19 pages, 8 figures

Scientific paper

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 $T(j) \equiv {}/{m_j}$, 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 $N \rightarrow \infty$. 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 $N \rightarrow \infty$.

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