Influence of heat bath on the heat conductivity in disordered anharmonic chain
We study heat conduction in a one-dimensional disordered anharmonic chain with arbitrary heat bath by using extended Ford, Kac and Mazur (FKM) formulation, which satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat conductivity κ is obtained, from which the asymptotic system-size (N) dependence is extracted. It shows κ∼Nα. As a special case we give the expression that κ∼N1/2 for free boundaries, and κ∼ N-1/2 for fixed boundaries, from which we can get the conclusion that the momentum conservation is a key factor of the anomalous heat conduction. Comparing with different ∇T, the heat conductivity shows large difference between the linear system and the nonlinear system.
PACS.44.10.+i Heat conduction 05.70.Ln Nonequilibrium and irreversible thermodynamics 05.60.Gg Quantum transport 05.45.Ac Low-dimensional chaos
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