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Methods of Spectral Analysis in Mathematical Physics pp 69–87Cite as

Semiclassical Results for Ideal Fermion Systems. A Review

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 186))

Abstract

Ideal Fermion systems represent an issue of great recent interest. They consist of N-Fermion gases without interaction but subject to an exterior field or potential. In this paper we review recent studies of such systems in the following situations:

  • the low temprerature behavior of confined fermion gases in contact with an exterior reservoir

  • the action of a magnetic field on two-dimensional electronic devices

  • the transport and dissipation for time-dependent scatterers connected to several leads, known as “quantum pumps”.

The response of these different systems under the influence of the exterior potential or field is considered. In the first situation the response is calculated in terms of the “dynamical susceptibility” in the linear response framework, which yields a generalized Kubo formula. In the second situation the response is expressed by the magnetic susceptibility and the magnetization which are estimated semiclassically for various regimes of the temperature as compared with powers of the Planck constant. In the last situation the response is a measurable current estimated in an adiabatic framework.

All these results are contained by a series of papers by D. Robert and myself, and in recent works by Avron, Elgart, Graf and Sadun.

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Authors and Affiliations

  1. IPNL, Bâtiment Paul Dirac, Université Lyon-1, 4 rue Enrico Fermi, F-69622, Villeurbanne Cedex, France

    Monique Combescure

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  1. Monique Combescure
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Editor information

Editors and Affiliations

  1. Institut of Mathematics, Polish Academy of Sciences, ul. Sw. Tomasza 30/7, 31-027, Krakow, Poland

    Jan Janas

  2. Department of Mathematics, Lund Institute of Technology, 221 00, Lund, Sweden

    Pavel Kurasov

  3. Department of Mathematical Physics, St. Petersburg State University, Ulyanovskaya 1, 198904, St. Petersburg, Russia

    Sergei Naboko

  4. Department of Mathematics South Kensington Campus, Imperial College London, SW7 2AZ, London, UK

    Ari Laptev

  5. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Ari Laptev

  6. Department of Mathematics, University of Alabama, 452 Campbell Hall, Birmingham, AL, 35294-1170, USA

    Günter Stolz

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Combescure, M. (2008). Semiclassical Results for Ideal Fermion Systems. A Review. In: Janas, J., Kurasov, P., Naboko, S., Laptev, A., Stolz, G. (eds) Methods of Spectral Analysis in Mathematical Physics. Operator Theory: Advances and Applications, vol 186. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8755-6_4

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