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Nanosystems: Physics, Chemistry, Mathematics, 2015, Volume 6, Issue 2, Pages 224–243
DOI: https://doi.org/10.17586/2220-8054-2015-6-2-224-243
(Mi nano937)
 

This article is cited in 2 scientific papers (total in 2 papers)

Time-dependent quantum circular billiard

D. B. Babajanova, D. U. Matrasulovab, Z. A. Sobirovac, S. K. Avazbaevd, O. V. Karpovaab

a National University of Uzbekistan, Tashkent, Uzbekistan
b Turin Polytechnic University in Tashkent, 17. Niyazov Str., 100095, Tashkent, Uzbekistan
c Tashkent Financial Institute, 60A, Amir Temur Str., 100000 Tashkent, Uzbekistan
d ARC Centre for Antimatter-Matter Studies, Department of Applied Physics, Curtin University, G.P.O. Box U1987, Perth 6845, Australia
Full-text PDF (388 kB) Citations (2)
Abstract: The motion of a quantum particle in a time-dependent circular billiard is studied on the basis of the Schrödinger equation with time-dependent boundary conditions. The cases of monotonically expanding (contracting), non-harmonically, harmonically breathing circles the case when billiard wall suddenly disappears are explored in detail. The exact analytical solutions for monotonically expanding and contracting circles are obtained. For all cases, the time-dependence of the quantum average energy is calculated. It is found that for an harmonically breathing circle, the average energy is time-periodic in the adiabatic regime with the same period as that of the oscillation. For intermediate frequencies which are comparable with the initial frequency of the particle in unperturbed billiard, such periodicity is broken. However, for very high frequencies, the average energy once again becomes periodic. A qualitative analysis of the border between adiabatic and non-adiabatic regimes is provided.
Keywords: quantum billiards, Schrödinger equation.
Funding agency Grant number
Volkswagen Foundation I/82 136
This work is supported in part by a grant of Volkswagen Foundation (N r. I/82 136).
Received: 02.02.2015
Bibliographic databases:
Document Type: Article
PACS: 03.65.Ge
Language: English
Citation: D. B. Babajanov, D. U. Matrasulov, Z. A. Sobirov, S. K. Avazbaev, O. V. Karpova, “Time-dependent quantum circular billiard”, Nanosystems: Physics, Chemistry, Mathematics, 6:2 (2015), 224–243
Citation in format AMSBIB
\Bibitem{BabMatSob15}
\by D.~B.~Babajanov, D.~U.~Matrasulov, Z.~A.~Sobirov, S.~K.~Avazbaev, O.~V.~Karpova
\paper Time-dependent quantum circular billiard
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2015
\vol 6
\issue 2
\pages 224--243
\mathnet{http://mi.mathnet.ru/nano937}
\crossref{https://doi.org/10.17586/2220-8054-2015-6-2-224-243}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000219891700011}
\elib{https://elibrary.ru/item.asp?id=23238126}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Nanosystems: Physics, Chemistry, Mathematics
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