Infinite ascension limit: horocyclic chaos

DOI10.1016/J.GEOMPHYS.2020.104053arXiv2003.01388MaRDI QIDQ6336017

Mikhail Dubashinskiy

Publication date: 3 March 2020

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.

Mathematics Subject Classification ID

Wave scattering in solid mechanics (74J20) Forms of half-integer weight; nonholomorphic modular forms (11F37) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

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