标题： 量子力学和经典力学中的Liouville不变性 显示英文标题

标题： Liouville invariance in quantum and classical mechanics

摘要： 密度矩阵和海森堡形式的量子力学——对于幺正演化——直接来自薛定谔方程。 然而，相应的演化算符的对称性，李乌维尔算子 L=i[.,H]，不必局限于哈密顿量 H 的对称性。这是由于 L 仅涉及本征能量差，即使能量本身不简并，这些能量差也可能是简并的。 值得注意的是，这种可能性在文献中很少被提及，更没有被进一步探讨。 我们考虑一个涉及介观约瑟夫森器件的例子，但分析仅假设熟悉基本的量子力学。 随后，显示出这样的 L 对称性更广泛存在，特别是在经典力学中也是如此。 讨论了该对称性在耗散系统和量子信息处理中的相关性。 显示英文摘要

摘要： The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This is due to L only involving eigenenergy_differences_, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has rarely been mentioned in the literature, and never pursued more generally. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such _L-symmetries_ are shown to occur more widely, in particular also in classical mechanics. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed.