Joseph E. Avron, Sven Bachmann, Gian Michele Graf, Israel Klich
Fredholm determinants and the statistics of charge transport
(94K, Latex 2e with 2 PS figures)
ABSTRACT. Using operator algebraic methods we show that the moment
generating function of charge transport in a system with
infinitely many non-interacting Fermions is given by a
determinant of a certain operator in the one-particle Hilbert
space. The formula is equivalent to a formula of Levitov
in the finite dimensional case and may be viewed as its
regularized form in general. Our result embodies two
fundamental principles in mesoscopic physics, namely, that
the transport properties are essentially independent of
the length of the leads and of the depth of the Fermi sea.