Fourier's Law: insight from a simple derivation

Details Fourier's Law: insight from a simple derivation Fourier's Law: insight from a simple derivation

2008-12-27

arxiv.org/abs/0812.4774v2

Phys. Rev. E 79, 042101 (2009)

Physics

Condensed Matter

Statistical Mechanics

4+ pages, references and discussions added

Scientific paper

The onset of Fourier's law in a one-dimensional quantum system is addressed via a simple model of weakly coupled quantum systems in contact with thermal baths at their edges. Using analytical arguments we show that the crossover from the ballistic (invalid Fourier's law) to diffusive (valid Fourier's law) regimes is characterized by a thermal length-scale, which is directly related to the profile of the local temperature. In the same vein, dephasing is shown to give rise to a classical Fourier's law, similarly to the onset of Ohm's law in mesoscopic conductors.

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