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Dissipative Dynamics in Semiconductors at Low Temperature

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Abstract

A mathematical model is introduced which describes the dissipation of electrons in lightly doped semi-conductors. The dissipation operator is proved to be densely defined and positive and to generate a Markov semigroup of operators. The spectrum of the dissipation operator is studied and it is shown that zero is a simple eigenvalue, which makes the equilibrium state unique. Also it is shown that there is a gap between zero and the rest of its spectrum which makes the return to equilibrium exponentially fast in time.

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Notes

  1. It should actually be given by the Bose-Einstein distribution (e βε−1)−1. But if βε≫1 it follows that (e βε−1)−1≈e −βε.

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Acknowledgements

This work benefited from the NSF grants DMS-0600956 and DMS-0901514. Part of this work was done in Bielefeld with the support of the SFB 701 “Spectral Structures and Topological Methods in Mathematics” during the Summers 2009 and 2010. G.A. and C.S. thank the School of Mathematics at the Georgia Institute of Technology for support during the Spring 2009.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    George Androulakis

  2. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, 30332-0160, USA

    Jean Bellissard

  3. Department of Mathematics, University of California Irvine, Irvine, CA, 92697-3875, USA

    Christian Sadel

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  1. George Androulakis
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  2. Jean Bellissard
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  3. Christian Sadel
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Correspondence to George Androulakis.

Additional information

J. Bellissard and C. Sadel were supported by NSF grants DMS-0600956 and DMS-0901514.

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Androulakis, G., Bellissard, J. & Sadel, C. Dissipative Dynamics in Semiconductors at Low Temperature. J Stat Phys 147, 448–486 (2012). https://doi.org/10.1007/s10955-012-0454-5

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