Comptes Rendus
Mathematical Physics/Functional Analysis
The ground state problem for a quantum Hamiltonian describing friction
Comptes Rendus. Mathématique, Volume 339 (2004) no. 2, pp. 151-156.

In this Note, 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.

Dans cette Note, on considère la version quantique d'un modèle hamiltonien décrivant le phénomène de frottement. Ce modèle consiste en une particule en interaction avec un réservoir de bosons représentant un milieu homogène dans lequel la particule se déplace. On montre que si la particule est confinée, alors le hamiltonien admet un état fondamental si et seulement si une condition infrarouge adaptée est satisfaite. Cette dernière est violée dans le cas d'un frottement linéaire, mais satisfaite lorsque la force de frottement est proportionnelle à une puissance plus élevée de la vitesse de la particule.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.05.005

Laurent Bruneau 1

1 Department of Mathematical Methods in Physics, Warsaw University, Hoza 74, 00-682, Warszawa, Poland
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Laurent Bruneau. The ground state problem for a quantum Hamiltonian describing friction. Comptes Rendus. Mathématique, Volume 339 (2004) no. 2, pp. 151-156. doi : 10.1016/j.crma.2004.05.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.05.005/

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