Heat conduction in the disordered harmonic chain revisited

Abstract

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'' $J\sim 1/N$.

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

References in corpus (2)

• Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses
• Can disorder induce a finite thermal conductivity in 1D lattices?

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