A many-fermion generalization of the Caldeira-Leggett model
Abstract
We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green's functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, that results in complete thermalization of the system.
Keywords
Cite
@article{arxiv.cond-mat/0409401,
title = {A many-fermion generalization of the Caldeira-Leggett model},
author = {Florian Marquardt and D. S. Golubev},
journal= {arXiv preprint arXiv:cond-mat/0409401},
year = {2007}
}
Comments
v3: fixed pdf problem; v2: added exact formula (Eq. 42) for Green's function and discussion of equilibrium density matrix (new Fig. 2); 10 figures, 21 pages, see quant-ph/0305098 for brief version of some of these results