Chruściński Dariusz
Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland.
Chaos. 2021 Feb;31(2):023110. doi: 10.1063/5.0036620.
We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard Gorini-Kossakowski-Lindblad-Sudarshan generator. These two processes commute and both of them commute with the unitary evolution controlled by the systems Hamiltonian. The corresponding memory kernel gives rise to semi-Markov evolution of the diagonal elements of the density matrix. However, the corresponding evolution needs not be completely positive. The role of decoherence generator is to restore complete positivity. Hence, to pose the dynamical problem, one needs two processes generated by classical semi-Markov memory kernel and purely quantum decoherence generator. This scheme is illustrated for a qubit evolution.
我们提供了一类超越马尔可夫半群的量子演化。这类演化由一种类似混合戴维斯的生成器控制，使得耗散由合适的记忆核控制，退相干由标准的戈里尼 - 科萨克夫斯基 - 林德布拉德 - 苏达山生成器控制。这两个过程相互对易，并且它们都与由系统哈密顿量控制的幺正演化对易。相应的记忆核导致密度矩阵对角元素的半马尔可夫演化。然而，相应的演化不一定是完全正定的。退相干生成器的作用是恢复完全正定性。因此，为了提出动力学问题，需要由经典半马尔可夫记忆核和纯量子退相干生成器产生的两个过程。针对量子比特演化对该方案进行了说明。
