A new method for quantum processes in fermionic heat baths

Abstract

The general path-integral formalism for real-time dynamics for a quantum system in a fermionic environment proposed previously is investigated by using a new method called local adiabatic transformation. This method is based on the observation that in the long-time limit (the time scale of the system is much larger than that of the environment, typically characterized by the inverse of the cutoff frequency of the environment), most degrees of freedom of the environment will follow the dynamics adiabatically. This feature is utilized by transforming the original problem of coordinate coupling into a problem of velocity coupling. This is achieved by making some simple unitary transformation on the fermion field (before path-integrating out of that field). By doing perturbations on the new problem, all the previous important results are recovered. Further-more, generalizations to more realistic situations [for example, a particle traveling over a large distance and coupled to a Fermi gas through the phase factor exp(ik·R) (the coupling may involve many channels of angular momentum)] are considered and significant results obtained.