林德布拉德方程的熵梯度结构及量子系统与宏观模型的耦合
An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models
摘要：
我们证明了有限维Hilbert空间上满足关于热平衡态的细致平衡条件的所有Lindblad算子（即量子半群的生成元）都可以写成关于相对熵的梯度系统.我们还讨论了与宏观系统，无论是作为阻尼哈密顿系统与恒温或作为通用系统的耦合。特别地，我们讨论了耦合到宏观载流子的量子点的耦合。
英文摘要：
We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems. In particular we discuss the coupling of a quantum dot coupled to macroscopic charge carriers.
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