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Equilibrium Analysis of a Dissipative Fermion System

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Spectral Analysis of Quantum Hamiltonians

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 224))

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Abstract

A model of an open system of fermion particles submitted to a constant magnetic field and immersed in a reservoir of phonons is considered within this article. The focus is set on the large time behavior of this system, the purpose being to illustrate the methods of Quantum Markov Semigroup Theory. After providing sufficient conditions to ensure the existence of the semigroup, this report goes through the construction of stationary states, the analysis of the equilibrium via detailed balance conditions. Ergodic behavior of the system is obtained as a byproduct of the above.

Mathematics Subject Classification (2000). 81S25, 81S22, 82C22, 82C70, 60H30.

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Authors and Affiliations

  1. Centro de Análisis Estocástico y Aplicaciones Facultad de Matemáticas, Universidad Católica de Chile, Vicuña Mackenna 4860, 7820436, Macul, Santiago, Chile

    Rolando Rebolledo

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  1. Rolando Rebolledo
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Editors and Affiliations

  1. , Departamento de Física, P. Universidad Católica de Chile, Santiago, 22, Chile

    Rafael Benguria

  2. , Departamento de Matemáticas, Universidad de Chile, Las Palmeras, Nuñoa 3425, Santiago, Chile

    Eduardo Friedman

  3. , Departamento de Matemática, Universidad de Chile, Las Palmeras, Nuñoa 3425, Santiago, Chile

    Marius Mantoiu

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Rebolledo, R. (2012). Equilibrium Analysis of a Dissipative Fermion System. In: Benguria, R., Friedman, E., Mantoiu, M. (eds) Spectral Analysis of Quantum Hamiltonians. Operator Theory: Advances and Applications, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0414-1_13

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