Spectral analysis of a model for quantum friction

De Bievre, Stephan; Faupin, Jérémy; Schubnel, Baptiste

Document type :

Pré-publication ou Document de travail

Title :

Spectral analysis of a model for quantum friction

Author(s) :

De Bievre, Stephan [Auteur]

Quantitative methods for stochastic models in physics [MEPHYSTO]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Faupin, Jérémy [Auteur]
Institut Élie Cartan de Lorraine [IECL]
Schubnel, Baptiste [Auteur]
Institut Élie Cartan de Lorraine [IECL]

HAL domain(s) :

Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity ...
Show more >An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude which is typically proportional to a power of its speed. We study here the quantum equivalent of a classical Hamiltonian model for this friction phenomenon that was proposed in [11]. More precisely, we study the spectral properties of the quantum Hamiltonian and compare the quantum and classical situations. Under suitable conditions on the infrared behaviour of the model, we prove that the Hamiltonian at fixed total momentum has no ground state except when the total momentum vanishes, and that its spectrum is otherwise absolutely continuous.Show less >

Language :

Anglais

Collections :