Dissipative dynamics in semiconductors at low temperature

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.

36 pages, 1 figure

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• Spectral Gap and Exponential Decay of Correlations
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• Mott law as lower bound for a random walk in a random environment
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Cited by in corpus (8)

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• Disordered Crystals from First Principles II: Transport Coefficients
• Quantum Brownian motion induced by thermal noise in the presence of disorder
• Mapping the Current-Current Correlation Function Near a Quantum Critical Point
• A groupoid approach to interacting fermions
• Miller-Abrahams random resistor network, Mott random walk and 2-scale homogenization
• Stochastic homogenization in amorphous media and applications to exclusion processes