Mazur界和Suzuki等式的再认识
Revisiting the Mazur bound and the Suzuki equality
摘要：
在为数不多的已知严格的结果与时间有关的平衡的相关性，重要的是了解输运性质，是马祖尔界和铃木平等。Mazur不等式给出了一个关于可观测量的含时自相关函数的长时间平均值的下界，该下界是关于包含守恒量的平衡关联函数的。另一方面，铃木提出了量子系统的精确等式。在本文中，我们讨论了这两个结果之间的关系，特别是，寻找类似的经典系统的铃木结果。这就要求我们研究什么构成了一套完整的守恒量所需的饱和马祖尔界限。我们提出的分析参数，以及说明性的数值结果，从一些不同的系统。我们的例子包括几个自由度的系统，以及多粒子可积模型，自由和相互作用。
英文摘要：
Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.
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