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The Ground State Problem for a Quantum Hamiltonian Model Describing Friction

Published online by Cambridge University Press:  20 November 2018

Laurent Bruneau
Laurent Bruneau*
Affiliation:
Laboratoire AGM, Université de Cergy-Pontoise, Site Saint-Martin, B.P. 222, 95302 Cergy-Pontoise, France email: laurent.bruneau@u-cergy.fr
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Abstract

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In this paper, we consider the quantum version of a Hamiltonian model describing friction. This model consists of a particle which interacts with a bosonic reservoir representing a homogeneous medium through which the particle moves. We show that if the particle is confined, then the Hamiltonian admits a ground state if and only if a suitable infrared condition is satisfied. The latter is violated in the case of linear friction, but satisfied when the friction force is proportional to a higher power of the particle speed.

Keywords

81Q1046N50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 5 , 01 October 2007 , pp. 897 - 916
Copyright
Copyright © Canadian Mathematical Society 2007

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