The Bakerian Lecture, 1987. Quantum chaology
The Bakerian Lecture, 1987. Quantum chaology
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贝克里安讲座，1987 年。量子混沌学
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发表时间：
1987
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通讯作者：
M. Berry
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作者：
M. Berry
有界或受驱动的经典系统经常表现出混沌（持续存在的指数不稳定性），但它们的量子对应系统却不会。然而，在半经典极限中出现了新的量子行为机制，这取决于经典轨道是规则的还是混沌的，这激发了以下定义。定义。量子混沌学研究的是经典运动表现为混沌的系统的半经典但非经典的行为特征。能量等级的统计数据说明了这一点。在与平均水平间距相当的尺度上（N自由度为hN阶），这些归为普世性类：对于经典混沌系统，统计量是随机矩阵的统计量（实对称或复厄米特，取决于是否存在时间反转对称性）；对于经典规则粒子，统计量是泊松的。在更大的尺度上（h阶，即经典小但半经典大），普适性就失效了。这些现象是通过用经典闭轨道表示光谱来解释的：普遍的光谱行为起源于很长的轨道；非普遍行为只依赖于短的行为。
Bounded or driven classical systems often exhibit chaos (exponential instability that persists), but their quantum counterparts do not. Nevertheless, there are new régimes of quantum behaviour that emerge in the semiclassical limit and depend on whether the classical orbits are regular or chaotic, and this motivates the following definition. Definition. Quantum chaology is the study of semiclassical, but nonclassical, behaviour characteristic of systems whose classical motion exhibits chaos. This is illustrated by the statistics of energy levels. On scales comparable with the mean level spacing (of order hN for N freedoms), these fall into universality classes: for classically chaotic systems, the statistics are those of random matrices (real symmetric or complex hermitian, depending on the presence or absence of time-reversal symmetry); for classically regular ones, the statistics are Poisson. On larger scales (of order h, i. e. classically small but semiclassically large), universality breaks down. These phenomena are being explained by representing spectra in terms of classical closed orbits: universal spectral behaviour has its origin in very long orbits; non-universal behaviour depends only on short ones.