Spin dynamics and violation of the fluctuation dissipation theorem in a non-equilibrium ohmic spin boson model

Abstract

We present results for the dynamics of an impurity spin coupled to a magnetic field and to two ohmic baths which are out-of equilibrium due to the application of a bias voltage. Both the non-equilibrium steady state and the rate constants describing the approach to steady state are found to depend sensitively on the relative strengths of a magnetic field and a voltage dependent decoherence rate. Computation of physical quantities including the frequency dependent ratio of response to correlation functions and the probabilities of the two spin states allows the extraction of voltage dependent effective temperatures. The temperatures extracted from different quantities differ from one another in magnitude and their dependence on parameters, and in general are non-monotonic.