【摘要】 一个作循环周期缓慢演变的含时Hamiltonian量子系统,在演变过程中波函数除了熟悉的动力学相因子外,还附加一个非动力学性质相因子exp{iγn(t)}。笔者从含时规范变换出发,对该量子系统出现的非动力学相作了深入分析与研究,研究结果表明:当系统未完成一个周期的演变时,可以出现一个"不可积"的非动力学相;而只有当系统完成一个周期的演变,才可得到"可积"的相位—Berry相,这种相位具有"周期含时规范变换"不变性,因而存在物理观察效应。进而以核磁共振为例对Berry相的"拓扑性"作了完整的说明。更多还原

【Abstract】 A quantum system with time-dependent Hamiltonian which transports slowly will acquire an undynamic phase factor exp{ iγ n(t) } factor during evolution in addition to a dynamic phase factor. By means of time-dependent gauge transformation, we do a thorough study on undynamic phase which emerge in the quantum system. The results show that the system will gain an non-integrable phase when a periodic evolution doesn’t accomplished; however, only when the system achieves a periodic evolution, an integrable phase will be acquire, namely Berry phase, and the phase is invariable under periodic time-dependent gauge transformation, thereby it is observable. Accordingly, we do a general interpretation on the topological property of Berry’s phase as an example of NMR.更多还原