Dynamics of a two-level system coupled to a dissipative bath: Comparisons of analytical theories with Monte Carlo simulation

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Abstract
We apply the quantum dynamical Monte Carlo technique to the calculation of the complex time correlation function of the flux through a SQUID, and compare the results with those of three representative theories: a random phase approximation (RPA), an effective adiabatic approximation (EA), and an optimized random phase approximation (ORPA). The RPA quickly becomes unreliable as the damping is increased beyond a negligible amount. For small coupling, the variational information contained in the EA theory results in superior predictions of initial decay rates, but for moderate coupling the inherent nonergodicity of the theory leads to incorrect results for the long time behavior of the correlation function. The ORPA fails to renormalize the initial frequency properly, but succeeds in predicting the correct qualitative behavior even at moderately large values of the damping. This illustrates the power of the QDMC as a benchmark against which to test approximations, and as a bridge between their regions of applicability.