Failure of the Wiedemann-Franz law in mesoscopic conductors

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.