Berry's Phase
Berry's Phase
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DOI：
10.1146/annurev.pc.41.100190.003125
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发表时间：
1990
影响因子：
14.7
通讯作者：
J. Zwanziger;M. Koenig;A. Pines
中科院分区：
文献类型：
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作者：
J. Zwanziger;M. Koenig;A. Pines
贝里阶段 (1, 2) 是完整性的一个例子，即当表征系统的其他变量或参数返回到其初始值 (3, 4) 时，某些变量发生变化的程度。图 1 显示了经典完整学的一个简单案例；粒子（具有由箭头指示的切向量）在球体表面上移动，从北极开始和结束，其局部不绕垂直于表面的轴旋转。然而，由于曲面上的这种平行传输，当粒子返回到其原始位置时，可以累积旋转。4以类似的方式，量子系统的状态向量可以在状态空间中经历循环演化时“旋转”，从而累积同调。贝里阶段最普遍的背景来自于将一个系统（也许是宇宙）划分为多个部分。问题是，当一个子系统经历循环演化时，我们能对整个系统说什么呢？通常，人们可能会尝试求解整个系统的运动方程，例如薛定谔方程；事实上，通过认识到以下因素的作用，我们通常可以更好地回答问题：
Berry's phase (1, 2) is an example of holonomy, the extent to which some variables change when other variables or parameters characterizing a system return to their initial values (3, 4). A simple case of classical holonomy is shown in Figure 1; a particle (with a tangent vector indicated by an arrow) moves on the surface of a sphere, beginning and ending at the north pole, in such a way that locally it docs not rotate about an axis perpendicular to the surface. As a consequence of this parallel transport on the curved surface, however, a rotation can be accumulated when the particle returns to its original position.4 In a similar way, the state vector of a quantum system can "rotate" as it undergoes a cyclic evolution in state space, thereby accumulating a ho)onomy. The most general context for Berry's phase arises from the division of a system (perhaps the universe) into parts; the question is, what can we say about the full system, when a subsystem undergoes a cyclic evolution? Typically one might attempt a solution to the equations of motion, for example the Schrodinger Equation, for the full system; the fact that we can often do better in answering the question by recognizing the role of