Quantum dissipation of arbitrary strength from coupling to fermions

Abstract

A single degree of freedom, analogous to the coordinate of a particle, is coupled to the density fluctuations of a filled sea of fermions. The fermions live in one spatial dimension and have a linear energy-momentum relation, as may be appropriate in the vicinity of the Fermi surface. By using the equivalence of fermions and bosons in one space dimension, the author shows that the classical limit of the above theory leads to a Langevin equation for the coordinate of the 'particle' in which there are no constraints on the strength of the friction constant. This is in distinction to existing models of fermionic heat baths which have upper limits on the value of the friction constant. The non-classical behaviour of the system is studied by determining the reduced equilibrium density matrix of the particle. The fermions, described by a functional integral over Grassmann fields, are uncoupled from the particle by a change of variables which is equivalent to a chiral gauge transformation. This generates a non-trivial Jacobian which is evaluated in an appendix and leads, in an appropriate limit, to identical results to those found by Caldeira and Leggett (1983) for an oscillator heat bath.