Infinite ascension limit: Horocyclic chaos

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Infinite ascension limit: Horocyclic chaos. / Дубашинский, Михаил Борисович.

In: Journal of Geometry and Physics, Vol. 161, 104053, 03.2021.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ac45c939594048beae064940bd13ccec,

title = "Infinite ascension limit: Horocyclic chaos",

abstract = "What will be if, given a pure stationary state on a compact hyperbolic surface, we start applying raising operator every ”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 possessing a simple geometric description. 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.",

keywords = "quantum unique ergodicity, raising and lowering operators, singularity propagation, Ergodic theory, Lagrangian and Hamiltonian mechanics, Quantum dynamical and integrable systems, Quantum unique ergodicity, Raising and lowering operators, Singularity propagation",

author = "Дубашинский, {Михаил Борисович}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2021",

month = mar,

doi = "10.1016/j.geomphys.2020.104053",

language = "English",

volume = "161",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Infinite ascension limit: Horocyclic chaos

AU - Дубашинский, Михаил Борисович

PY - 2021/3

Y1 - 2021/3

N2 - What will be if, given a pure stationary state on a compact hyperbolic surface, we start applying raising operator every ”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 possessing a simple geometric description. 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.

AB - What will be if, given a pure stationary state on a compact hyperbolic surface, we start applying raising operator every ”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 possessing a simple geometric description. 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.

KW - quantum unique ergodicity, raising and lowering operators, singularity propagation

KW - Ergodic theory

KW - Lagrangian and Hamiltonian mechanics

KW - Quantum dynamical and integrable systems

KW - Quantum unique ergodicity

KW - Raising and lowering operators

KW - Singularity propagation

UR - https://arxiv.org/abs/2003.01388

UR - http://www.scopus.com/inward/record.url?scp=85098964916&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/d16e73de-2a52-3ad7-8026-9c61ee484464/

U2 - 10.1016/j.geomphys.2020.104053

DO - 10.1016/j.geomphys.2020.104053

M3 - Article

VL - 161

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

M1 - 104053

ER -

ID: 75212413