Fourier's Law: insight from a simple derivation

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 (vali...

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Bibliographic Details
Published inarXiv.org
Main Authors Dubi, Y, M Di Ventra
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.02.2009
Subjects
Conductors
Crossovers
Fourier law
Ohm's Law
Physics - Mesoscale and Nanoscale Physics
Physics - Statistical Mechanics
Quantum theory
Thermal baths
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0812.4774