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——对于幺正演化——直接来自薛定谔方程。 尽管相应演化算符的对称性，李乌维尔算符$\mathcal{L}=i[\cdot,H]$，不必仅限于哈密顿量$H$的对称性。 这是由于$\mathcal{L}$仅涉及本征能量的差值，即使能量本身不简并，这些差值也可能简并。 值得注意的是，这种可能性在文献中从未被研究过。 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$\mathcal{L}$-对称性更广泛存在，特别是在经典力学中也是如此。 该对称性在耗散系统和量子信息处理中的相关性被简要讨论。 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 $\mathcal{L}=i[\cdot,H]$, need not be limited to those of the Hamiltonian $H$. This is due to $\mathcal{L}$ only involving eigenenergy _differences_, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has never been investigated in the literature. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such _$\mathcal{L}$-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.