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arXiv · 2003.01388

Infinite ascension limit: horocyclic chaos

Mikhail Dubashinskiy
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Abstract

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.

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BibTeXRIS

Mikhail Dubashinskiy. 2020-03-03. Infinite ascension limit: horocyclic chaos. https://doi.org/10.1016/j.geomphys.2020.104053

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