角动量系统在外加旋转磁场下的非绝热Berry相

Non-adiabatic Berry phase of angular momentum system in a rotating magnetic field

利用 Mathematica软件求解了角动量 l=1的系统在强外加旋转磁场下的含时间 Schr dinger方程 ,得出了非绝热条件下的精确解 ,给出了任意初始态在非绝热条件下成为周期态的条件。比较绝热条件下瞬时态的 Berry相和非绝热过程的 Aharonov- Anandan相因子 ,发现在磁场缓慢旋转的极限下二者趋于一致。还利用算符分解方法给出了任意大l的量系统的解的形式 ,并对 l=1的情况得出了与 Mathe-matica精确解法同样的结果 ,从另一个角度给出了非绝热Berry相。

A software Mathematica was used to obtain an exact non-adiabatic solution to the time-dependent Schrodinger equation for an angular momentum l=1 system in a rotating magnetic field. Conditions are given for an arbitrary initial state in the non-adiabatic process to become a cyclic one. Comparison of the Berry phase for an adiabatic instantaneous state and the non-adiabatic Aharonov-Anandan phase shows that they tend to coincide in the limit of a slowly rotating field. The Operator Decomposition Scheme was used for an arbitrary angular momentum system to obtain the form of the solution. For the case of l=1, the result was the same as that given by Mathematica, thus exhibiting another formalism for the non-adiabatic Berry phase. This method can be generalized to study the topological phase factor of a coupled spin-chain model.