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Fredholm Determinants and the Statistics of Charge Transport

Avron, J. E. and Bachmann, S. and Graf, G. M. and Klich, I. (2008) Fredholm Determinants and the Statistics of Charge Transport. Communications in Mathematical Physics, 280 (3). pp. 807-829. ISSN 0010-3616. doi:10.1007/s00220-008-0449-x.

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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 and Lesovik in the finite dimensional case and may be viewed as its regularized form in general. Our result embodies two tenets often realized 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.

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Additional Information:© 2008 Springer. Received: 1 May 2007 Accepted: 20 August 2007 Published online: 13 March 2008. We would like to thank H. Araki, P. Deift, G. Dell’Antonio, G. Kottanattu, G. Lesovik and W. de Roeck for discussions. We also thank the Erwin Schrödinger Institute (Vienna) and the Lewiner Institute for Theoretical Physics at the Technion (Haifa) for hospitality.
Subject Keywords:mathematical physics; mesoscale and nanoscale physics
Issue or Number:3
Classification Code:MSC classes: 81V70; 47L90
Record Number:CaltechAUTHORS:20091013-193752273
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16334
Deposited By: Joy Painter
Deposited On:14 Oct 2009 16:26
Last Modified:08 Nov 2021 23:26

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