标题： 动态对称性和量子非绝热转变 显示英文标题

标题： Dynamic Symmetries and Quantum Nonadiabatic Transitions

摘要： 克勒默简并定理是量子力学中的一个基本结论。根据该定理，时间反演对称性使得半整数自旋系统的每一个能级至少双重简并，这意味着如果哈密顿量不显式依赖于时间，则简并态之间不存在跃迁或散射。我们将这一结果推广到显式时间相关的自旋哈密顿量的情形。我们证明了对于总自旋为半整数的自旋系统，如果其哈密顿量和演化时间区间在特定定义的时间反演操作下具有对称性，则任意初始态与其时间反演对应态之间的散射振幅精确为零。我们还讨论了该结果在多状态朗道-齐纳（Landau-Zener）理论中的应用。 显示英文摘要

摘要： Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. We generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. We also discuss applications of this result to the multistate Landau-Zener (LZ) theory.