Local Approximation for the Lossy Spin–boson Model

We are interested in the problem of coherent energy exchange in the spin-boson model augmented with loss, in the limit of infinite loss. This model is interesting because it predicts rapid coherent energy exchange under conditions when the transition energy of the two-level systems is much greater than the characteristic energy of the oscillator. Here we introduce the local approximation, in which we assume that the matrix elements change little when an energy exchange event occurs. This approximation results in a periodic system when a resonance condition is satisfied, which is much easier to solve than the original problem. We consider a model problem where we analyze the self-energy and indirect coupling matrix elements numerically and in the local approximation, with good agreement. Systematic results from the local approximation are obtained for the self-energy and indirect coupling matrix elements in models where 3, 5, 7, 9, and 11 quanta are exchanged. © 2011 ISCMNS. All rights reserved.