Heat conduction in the disordered harmonic chain revisited

Details Heat conduction in the disordered harmonic chain revisited Heat conduction in the disordered harmonic chain revisited

2001-05-04

arxiv.org/abs/cond-mat/0105085v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures, accepted for publication in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.86.5882

A general formulation is developed to study heat conduction in disordered harmonic chains with arbitrary heat baths that satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat current J is obtained, from which its asymptotic system-size (N) dependence is extracted. It is shown that the ``thermal conductivity'' depends not just on the system itself but also on the spectral properties of the fluctuation and noise used to model the heat baths. As special cases of our heat baths we recover earlier results which reported that for fixed boundaries $J \sim 1/N^{3/2}$, while for free boundaries $J \sim 1/N^{1/2}$. For other choices we find that one can get other power laws including the ``Fourier behaviour'' $J \sim 1/N$.

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