含时磁场中中性粒子和带电粒子的几何相位
Geometric phases for neutral and charged particles in a time-dependent magnetic field
摘要：
众所周知，自旋为1/2的中性粒子在任意磁场中运动的任何循环解都具有与自旋迹线所对的立体角成正比的非绝热几何相位。对于具有更高自旋的中性粒子，这对于具有特殊初始条件的循环解是正确的。然而，对于更一般的循环解，这并不成立。作为一个例子，我们考虑这种粒子在旋转磁场中运动的最一般的解决方案。如果系统的参数选择适当，则所有解都是循环的。非绝热几何相位和立体角都明确计算。结果表明，非绝热几何相位除了与立体角成比例的项外，还包含一个额外的项。当自旋为1/2时，额外项自动消失。然而，对于更高的自旋，它取决于初始条件。我们还考虑了碱性原子的价电子。对于任意强磁场中具有特殊初始条件的循环解，我们证明了非绝热几何相位是轨道和自旋角动量迹对着的两个立体角的线性组合.对于在强旋转磁场中的更一般的循环解，非绝热几何相位除了线性组合外还包含额外的项。
英文摘要：
It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geometric phase and the solid angle are both calculated explicitly. It turns out that the nonadiabatic geometric phase contains an extra term in addition to the one proportional to the solid angle. The extra term vanishes automatically for spin 1/2. For higher spin, however, it depends on the initial condition. We also consider the valence electron of an alkaline atom. For cyclic solutions with special initial conditions in an arbitrary strong magnetic field, we prove that the nonadiabatic geometric phase is a linear combination of the two solid angles subtended by the traces of the orbit and spin angular momenta. For more general cyclic solutions in a strong rotating magnetic field, the nonadiabatic geometric phase also contains extra terms in addition to the linear combination.
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