A Langevin canonical approach to the dynamics of two level systems. I. Populations and coherences

H. C. Peñate-Rodriguez, A. Dorta-Urra, P. Bargueno, G. Rojas-Lorenzo, S. Miret-Artes

Published 2012-07-13, updated 2012-11-22Version 2

A canonical framework for chiral two--level systems coupled to a bath of harmonic oscillators is developed to extract, from a stochastic dynamics, the thermodynamic equilibrium values of both the population difference and coherences. The incoherent and coherent tunneling regimes are analyzed for an Ohmic environment in terms of a critical temperature defined by the maximum of the heat capacity. The corresponding numerical results issued from solving a non-linear coupled system are fitted to approximate path--integral analytical expressions beyond the so-called non-interacting blip approximation in order to determine the different time scales governing both regimes.