A many-fermion generalization of the Caldeira-Leggett model

Details A many-fermion generalization of the Caldeira-Leggett model A many-fermion generalization of the Caldeira-Leggett model

2004-09-15

arxiv.org/abs/cond-mat/0409401v3

Phys. Rev. A 72, 022113 (2005)

Physics

Condensed Matter

Statistical Mechanics

v3: fixed pdf problem; v2: added exact formula (Eq. 42) for Green's function and discussion of equilibrium density matrix (new

Scientific paper

10.1103/PhysRevA.72.022113

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.

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