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

Abstract

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 $T(j)\equiv <p_j^2>/m_j$, 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 $N\to \infty$. 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 $N\to \infty$.

19 pages, 8 figures

References in corpus (6)

• Heat Transport in low-dimensional systems
• Heat transport in harmonic lattices
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Local Temperature and Universal Heat Conduction in FPU chains
• Heat conduction in disordered harmonic lattices with energy conserving noise
• Thermal Conductivity for a Noisy Disordered Harmonic Chain

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