Bath correlation functions for logarithmic-like spectral densities

Abstract

We analyze the short- and long-time behavior of the bath correlation function for open quantum systems interacting with thermal baths. The spectral densities under study are ohmic-like at low frequencies, exhibit possible perturbations of the low-frequency power-law profiles and are arbitrarily shaped at higher frequencies. The low-frequency perturbations are provided by arbitrarily positive or negative powers of logarithmic forms as additional factors for the power laws of the ohmic-like spectral densities. If the spectral density decays sufficiently fast at high frequencies the short-time behavior of the bath correlation function is algebraic. The model provides long-time relaxations of the bath correlation function which are arbitrarily faster or slower than inverse power laws. In fact, the long-time relaxations are described by inverse power laws and by arbitrary powers of logarithmic forms as additional factors. Such relaxations are regularly related to the low-frequency structure of the spectral density, except for even or odd natural values of the ohmicity parameter. In these exceptional conditions the long-time relaxations of the bath correlation function are faster than those obtained via the regular relation.