标题： 物理学中的新对称性？ 量子力学和经典力学中的Liouville不变性 显示英文标题

标题： A new symmetry in physics? Liouville invariance in quantum and classical mechanics

摘要： 密度矩阵和海森堡形式的量子力学可以——对于幺正演化——直接从薛定谔方程推导出来。 然而，相关演化算符——李乌维尔算符L——的对称性不必仅限于从相应哈密顿量继承的对称性。 这是由于L仅涉及本征能量差，即使能量本身不一致，这些差也可能一致。 值得注意的是，这种可能性尚未在文献中被研究。 我们考虑一个涉及介观约瑟夫森器件的例子，但分析仅假设熟悉量子力学的矩阵形式。 随后，该现象被证明更为普遍，并且其经典极限得到了阐明。 简要讨论了该对称性对耗散系统和量子信息处理的相关性。 显示英文摘要

摘要： The density-matrix and Heisenberg formulations of quantum mechanics can-for unitary evolution be directly derived from the Schr"odinger equation. However, the symmetries of the pertinent evolution operator-the Liouvillian L-need not be limited to those inherited from the corresponding Hamiltonian. This is due to L only involving the eigenenergy_differences_, which can coincide even if the energies themselves do not. Remarkably, this possibility has not yet been investigated in the literature. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with the matrix formulation of quantum mechanics. Subsequently, the phenomenon is shown to occur more widely, and its classical limit is elucidated. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed.