存在磁场时反对称的充要条件
Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields
摘要：
粒子系统的时间反演不变性（TRI）有许多结果，其中著名的Onsager倒易关系是统计力学的一个里程碑，可以追溯到1931年。由于长期以来人们认为（TRI）在存在磁场的情况下不成立，因此Casimir在1945年提出了对这种关系的修正。只是在过去的十年里，导致卡西米尔工作的严格的传统可逆性概念受到了质疑。然后发现可以使用其他对称性，这使得昂萨格互易关系保持不变。在本文中，我们提出了这一调查的经典哈密顿系统，大大增加了对称性的数量，产生TRI存在的磁场。本文首先推导了这类系统相空间上广义时间反演运算的最一般形式，其次给出了保证TRI的磁场的充分条件。最后，我们检查从统计力学和分子动力学的常见例子。我们的主要结果是，TRI持有比以前认为的更广泛的普遍性，部分解释了为什么没有实验违反Onsager关系迄今已被报道。
英文摘要：
Time reversal invariance (TRI) of particles systems has many consequences, among~which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the~strict traditional notion of reversibility that led to Casimir's work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We~first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.
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