Ground state for a quantum Hamiltonian describing friction

Jürg Martin Fröhlich, Zhou Gang, Avy Soffer

Laurent Bruneau

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.

B. A. Arbuzov

Laurent Bruneau

Abstract 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.

A. D. Jannussis, P. Filippakis, Th. Filippakis

Florian Marquardt

We discuss the importance of the real part of the Feynman-Vernon influence action for the analysis of dephasing and decay near the ground state of a system which is coupled to a bath. Using exactly solvable linear quantum dissipative systems, it is shown how the effects of the real and the imaginary part (describing friction and fluctuations, respectively) may cancel beyond lowest-order perturbation theory. The resulting picture is extended to a qualitative discussion of nonlinear systems and dephasing of degenerate fermions. We explain why dephasing rates will, in general, come out finite at zero temperature if they are deduced from the imaginary part of the action alone, a procedure which is reliable only for highly excited states.