Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems

Seligman, Thomas H.; Weidenmüller, Hans A.

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Journal Article

Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems

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Weidenmüller, Hans A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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http://iopscience.iop.org/1751-8121/44/20/205302
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1011.1339
(Preprint), 203KB

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Citation

Seligman, T. H., & Weidenmüller, H. A. (2011). Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems. Journal of Physics A: Mathematical and Theoretical, 44(20): 205302, pp. 1-14. Retrieved from http://arxiv.org/abs/1011.1339.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-2EF6-8

Abstract

We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.