关于通过松弛器李雅普诺夫动力学建模不可逆性的方法
On the modeling of irreversibility by relaxator Liouville dynamics
AI总结：
本文提出通过松弛器李雅普诺夫动力学建模不可逆性，结合微观可逆性与环境作用，推导出稳态方程和动力学方程，并推广线性响应理论。
摘要：
本文提出了一种从微观可逆性出发建模不可逆性的通用方法。时间$ t_s $用于跟踪系统相关自由度的时间远短于需要分辨所有涉及自由度谱的谱分辨时间$ t_e $。一个打破可逆性的松弛器在相关自由度的李雅普诺夫算子中凝聚。无关自由度作为系统的环境。不可逆的松弛器李雅普诺夫方程包含所有自由度的记忆效应和初始相关性。稳态被发现通常是唯一且不依赖初始条件的，例外是由于退化。平衡态位于松弛器的核中，产生一个稳态泡利主方程。单粒子密度的动力学方程作为松弛器李雅普诺夫动力学的特殊情况被构建。库布斯线性响应理论被推广到松弛器李雅普诺夫动力学，并与系统内的不可逆性相关联。在系统与环境之间弱耦合近似下，松弛器可被简化为环境相关性和双线性系统算子。马尔可夫近似将松弛器李雅普诺夫动力学转化为半群动力学。
英文摘要：
A general approach to modeling irreversibility starting from microscopic reversibility is presented. The time $t_s$ up to which relevant degrees of freedom of a system are tracked is extremely much shorter than the spectral resolution time $t_e$ that would be necessary to resolve the spectrum of all degrees of freedom involved. A relaxator that breaks reversibility condenses in the Liouville operator of the relevant degrees of freedom. The irrelevant degrees of freedom act as an environment to the system. The irreversible relaxator Liouville equation contains memory effects and initial correlations of all degrees of freedom. Stationary states turn out to be generically unique and independent of the initial conditions and exceptions are due to degeneracies. Equilibrium states lie in the relaxator's kernel yielding a stationary Pauli master equation. Kinetic equations for oneparticle densities are constructed as special cases of relaxator Liouville dynamics. Kubo's linear response theory is generalized to relaxator Liouville dynamics and related to irreversibility within the system. In a weak coupling approximation between system and environment the relaxator can be reduced to environmental correlations and bilinear system operators. Markov approximation turns the relaxator Liouville dynamics into a semi-group dynamics.
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