Journal of Statistical Physics

, Volume 147, Issue 2, pp 448–486 | Cite as

Dissipative Dynamics in Semiconductors at Low Temperature

  • George Androulakis
  • Jean Bellissard
  • Christian Sadel


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.


Dissipative quantum mechanics Equilibrium dynamics Markov process Lindbladian Many particle systems Electron transport in semiconductors 



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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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • George Androulakis
    • 1
  • Jean Bellissard
    • 2
  • Christian Sadel
    • 3
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  3. 3.Department of MathematicsUniversity of California IrvineIrvineUSA

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