Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion II

Abstract

The analysis of a strongly coupled harmonic quantum Brownian motion has been performed in [1] for a special class of spectral densities obtained as a generalization of the Drude model. In the present scenario, we extend the study of the strongly coupled harmonic quantum Brownian motion to regular spectral densities that are structured as sub-Ohmic at low frequencies and arbitrarily shaped at high frequencies. The bosonic environment is initially in the vacuum state unentangled from the coherent state of the main oscillator. As a generalization of the previous results, we obtain that the long time dynamics is determined uniquely by the initial condition and the low frequency structure of the spectral density. Also in the present framework, inverse power law regressions to the asymptotics appear. The position and the momentum tend to undamped oscillations. The number of excitations relaxes to its initial value with damped oscillations enveloped in inverse power law relaxations. For the momentum and the number of excitations the inverse power law decays become arbitrarily slow in critical configurations by approaching the upper bound of the sub-Ohmic regime. The critical frequencies of the main oscillator are determined by the first negative moment of the spectral densities. Differences with respect to the weak coupling regime arise.