What will be if, given a pure stationary state on a compact hyperbolic surface, we start applying raising operator every $\hbar$ "adiabatic" second? It turns that during adiabatic time comparable to 1 wavefunction will change as a wave traveling with a finite speed (with respect to the adiabatic time), whereas the semiclassical measure of the system will undergo a controllable transformation. If adiabatic time goes to infinity then, by quantized Furstenberg Theorem, the system will become quantum uniquely ergodic. Thus, infinite ascension of a closed system leads to quantum chaos.

中文翻译：

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无限提升极限：大循环混沌

如果在紧凑的双曲曲面上给定一个纯静止状态，我们开始每隔 $\hbar$“绝热”秒应用提升算子会怎样？结果表明，在与 1 波函数相当的绝热时间内，将作为以有限速度传播的波（相对于绝热时间）而变化，而系统的半经典测度将进行可控变换。如果绝热时间趋于无穷大，那么根据量化的弗斯滕伯格定理，系统将成为量子唯一遍历的。因此，封闭系统的无限提升会导致量子混沌。