We study the effect of mesoscopic fluctuations on the validity of the Wiedemannn-Franz (WF) law for quasi-one-dimensional metal wires and open quantum dots. At temperatures much less than the generalized Thouless energy, Ec, the WF law is satisfied for each specific sample, but as the temperature is raised through Ec, a sample-specific correction to the WF law of order 1/g appears (g is the dimensionless conductance) and then tends to zero again at kBT⪢Ec. The mesoscopic violation of the Weidemann-Franz law is even more pronounced in a ring geometry for which the Lorenz number exhibits $h∕e$ flux-periodic Aharonov-Bohm oscillations.
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Vavilov et al. (2005) studied this question.
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