论文标题
重新访问Mazur Bound和Suzuki平等
Revisiting the Mazur bound and the Suzuki equality
论文作者
论文摘要
对于时间依赖性平衡相关性的少数已知严格结果，对于理解运输特性很重要的是Mazur结合和铃木平等。 Mazur不平等在涉及保守量的平衡相关函数方面，对观测值的时间依赖性自动相关函数的长期平均值给出了下限。另一方面，铃木为量子系统提出了一个准确的平等性。在本文中，我们讨论了这两个结果之间的关系，尤其是寻找铃木结果的古典系统的类似物。这要求我们检查什么构成饱和Mazur结合所需的一组保守量。我们介绍了分析性论证以及许多不同系统的说明性数值结果。我们的示例包括具有很少自由度的系统以及自由和交互的许多粒子可集成模型。
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.
