Thermodynamics of a two-level system coupled to bosons

We study the thermodynamic properties of a system described by two discrete energy levels, coupled to a bath of phonons. We derive a discrete path-integral representation for the partition function that is convenient for numerical evaluation and allows us to calculate in a unified manner the model properties in the whole coupling range. As a function of the coupling strength the system exhibits a transition from the weak-coupling regime to the self-trapped state. In the weak-coupling regime there is a periodic motion, similar to the tunneling of a particle in a double-well potential. In the strong-coupling regime, the periodicity is lost and the motion turns into a stochastic process.