Two-Level System Coupled to Phonons: A Discrete Path-Integral Method

Abstract

A discrete path-integral representation for the partition function of a two-level tunneling system coupled to acoustic phonons is derived. This representation allows calculation of properties in the whole coupling range. As a function of the coupling there is an abrupt (ground-state) transition from the weak-coupling regime to the self-trapped state. From a moment analysis of the time-dependent spin-correlation function it follows that there is loss of phase coherence if the coupling exceeds the critical coupling. In this regime the mean effective tunneling rate vanishes linearly with temperature.