Bogolubov-van Hove极限下量子主方程修正中的非微扰效应
Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit
摘要：
本文研究了{ Gorini-Kossakowski-Sudarshan-林德布拉德方程在弱耦合极限下的微扰修正。本文讨论了零温旋波近似下的自旋玻色子模型。我们表明，扰动部分的密度矩阵满足时间无关的Gorini-Kossakowski-Sudarshan-林德布拉德方程的任意阶的扰动理论（如果所有的时刻的水库关联函数是有限的）。但是，为了在长时间内重现正确的渐近精度，应该使用与精确动力学不同的初始条件。此外，我们还证明了在某些共振条件下，这个主方程的初始条件甚至不是密度矩阵。
英文摘要：
We study the perturbative corrections to the { Gorini-Kossakowski-Sudarshan-Lindblad equation which arises in the weak coupling limit}. The spin-boson model in the rotating wave approximation at zero temperature is considered. We show that the perturbative part of the density matrix satisfies the time-independent Gorini-Kossakowski-Sudarshan-Lindblad equation for arbitrary order of the perturbation theory (if all the moments of the reservoir correlation function are finite). But to reproduce the right asymptotic precision at long times, one should use { an initial condition different} from the one for exact dynamics. Moreover, we show that the initial condition for this master equation even fails to be a density matrix under certain resonance conditions.
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