Abstract
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, ${E}_{c}$, the WF law is satisfied for each specific sample, but as the temperature is raised through ${E}_{c}$, 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 ${k}_{B}T⪢{E}_{c}$. 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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