Branch points in the complex plane and geometric phases.
Branch points in the complex plane and geometric phases.
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复平面和几何相中的分支点。
DOI：
10.1103/physreve.65.026217
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
I. Rotter
中科院分区：
文献类型：
--
作者：
I. Rotter
激光诱导简并态（LIDS）相当于S矩阵的双极点，它们是复平面（BPCP）上的分支点。这些分支点通过改变某些参数使它们绝热地围绕一个闭合回路，从而引起几何相位的变化。它们也引起众所周知的相位变化，出现在围绕一个恶魔点（DP）是一个奇点，与水平排斥有关。在这两种情况下，波函数交换，Phi(i) -> +/- iPhi(j不等于i)，在参数的临界值，状态避免交叉。这样一个临界点通过两次包围DP，但只有一次包围BPCP。因此，两种情况下的相变是不同的。第二次包围恢复波函数，包括两种情况下的相位（当BPCP与其他状态很好地隔离并且包围时间短于两种状态的寿命）。在一个闭合电路中，不同的干涉图沿相反的方向绝热地出现在周围的盖子上，这代表了贝里工作的完成。
Laser-induced degenerate states (LIDS) are equivalent to double poles of the S matrix that are branch points in the complex plane (BPCP). These branch points cause geometric phase changes by encircling them adiabatically around a closed circuit by varying certain parameters. They cause also the well-known phase changes appearing by encircling a diabolic point (DP) being a singularity associated with level repulsion. In both cases, the wave functions are exchanged, Phi(i) --> +/- iPhi(j not equal i), at the critical value of the parameter where the states avoid crossing. Such a critical point is passed twice by encircling a DP but only once by surrounding a BPCP. As a consequence, the phase changes are different in both cases. A second surrounding restores the wave functions including their phases in both cases (when the BPCP is well isolated from others and the time of encircling is shorter than the lifetime of the two states). The different interference pictures appearing in surrounding LIDS adiabatically in opposite directions on a closed circuit represent a completion of the work by Berry.