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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

Funded by The Danish National Research Foundation

MPS-RR 2004-12
March 2004

A rigorous proof for the Landauer-B üttiker formula

by: Horia Cornean, Arne Jensen, V. Moldoveanu


Recently, Avron et al in [1],. . . ,[5] shed new light on the question of quantum transport in mesoscopic samples coupled to particle reservoirs by semi-infinite leads. They rigorously treat the case when the sample undergoes an adiabatic evolution thus generating a current through the leads, and prove the so called BPT formula, see [9]. Using a discrete model, we complement their work by giving a rigorous proof of the Landauer-Büttiker formula, which deals with the current generated by an adiabatic evolution on the leads. As it is well known in physics, these formulae link the conductance coeffcients for such systems to the $S$-matrix of the associated scattering problem. As an application, we discuss the resonant transport through a quantum dot. The single charge tunneling processes are mediated by extended edge states simultaneosly localized near several leads.

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