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Funded by The Danish National Research Foundation
Abstract
Recently, Avron and his co-workers reopened the
question
of quantum transport in mesoscopic samples
coupled to particle reservoirs by semi-infinite leads. They give a
rigorous analysis of the case when the sample undergoes an adiabatic
evolution, which generates a current through the leads (the so called
BPT formula).
Using a tight-binding framework, 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 coefficients 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 simultaneously localized near several leads.
This work is joint with A. Jensen and V. Moldoveanu
Contact person:Arne Jensen.