Coherence dynamics in non-Markovian quantum Brownian motion

We present a perturbative non-Markovian extension to the Caldeira-Leggett 'system + environment model' of quantum Brownian motion, valid for general potentials and high temperatures. By expanding the Laplace transforms of the noise and dissipation kernels, we derive a master equation which describes the evolution of the reduced density matrix of a system of interest. By using a Fourier transform approach combined with the method of characteristics, an analytic solution is derived for the free particle case. The solution is plotted and discussed. The decoherence process is altered only slightly by the introduction of non-Markovianity, which we explain with a timescale argument. A new phenomenon which we term "lateral coherence" is observed. This is found to correspond to a resurgence of the l1-norm of coherence, at times much later than the decoherence time. We find that the coherence resurgence causes a transient reduction in the von Neumann entropy, and link this to an increasing body of work which makes links between non-Markovianity and entropy decrease. We show that this effect is independent of the high-frequency behaviour of the spectral density. Finally, we make some speculations about the relevance of our results in quantum biology, and suggest future avenues of research.