论文标题
在存在磁场的情况下，时间逆转对称性的必要条件
Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields
论文作者
论文摘要
颗粒系统的时间逆转不变性（TRI）具有许多后果，其中著名的Onsager互惠关系是一个可以追溯到1931年的统计力学中的里程碑。卡西米尔的工作受到质疑。然后发现可以使用其他对称性，从而使Onsager倒数关系可以保持而无需修改。在本文中，我们推进了对古典哈密顿系统的研究，从而大大增加了在存在磁场的情况下产生TRI的对称性数量。我们首先在此类系统的相空间上推断出广义时间逆转操作的最通用形式；其次，我们在磁场上表达足够的条件，以确保TRI。最后，我们研究了来自统计力学和分子动力学的常见例子。我们的主要结果是，TRI比以前认为的更广泛的通用性，部分解释了为什么迄今尚未涉及违反Onsager关系的实验性侵犯。
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.
