Abstract
A unified theory for minimum exponential-term ansatzes on bath correlation functions is proposed for numerically efficient and physically insightful treatments of non-Markovian environment influence on quantum systems. For a general Brownian oscillator bath of frequency Ω and friction ζ, the minimum ansatz results in the correlation function a bi-exponential form, with the effective Ω¯ and friction ζ¯ being temperature dependent and satisfying Ω¯/Ω=(ζ¯/ζ)1/2=r¯BO/rBO≤ 1, where r¯BO=ζ¯/(2Ω¯) and rBO=ζ/(2Ω). The maximum value of r¯BO=rBO can effectively be reached when kBT≥ 0.8Ω. The bi-exponential correlation function can further reduce to single-exponential form, in both the diffusion (rBO≫1) limit and the pre-diffusion region that could occur when rBO≥ 2. These are remarkable results that could be tested experimentally. Moreover, the impact of the present work on the efficient and accuracy controllable evaluation of non-Markovian quantum dissipation dynamics is also demonstrated.
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