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

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.