Time-dependent quantum circular billiard
https://doi.org/10.17586/2220-8054-2015-6-2-224-243
Abstract
The motion of a quantum particle in a time-dependent circular billiard is studied on the basis of the Schr¨odinger 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.
Supporting agencies: This work is supported in part by a grant of Volkswagen Foundation (Nr. I/82 136).
About the Authors
D. B. Babajanov
National University of Uzbekistan; Turin Polytechnic University in Tashkent
Uzbekistan
Uzbekistan
17. Niyazov Str., 100095, Tashkent
D. U. Matrasulov
National University of Uzbekistan; Turin Polytechnic University in Tashkent
Uzbekistan
Uzbekistan
17. Niyazov Str., 100095, Tashkent
Z. A. Sobirov
National University of Uzbekistan; Tashkent Financial Institute
Uzbekistan
Uzbekistan
60A, Amir Temur Str., 100000 Tashkent
S. K. Avazbaev
Curtin University
Australia
Australia
ARC Centre for Antimatter-Matter Studies, Department of Applied Physics
G.P.O. Box U1987, Perth 6845
O. V. Karpova
National University of Uzbekistan; Turin Polytechnic University in Tashkent
Uzbekistan
Uzbekistan
17. Niyazov Str., 100095, Tashkent
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Review
For citations:
Babajanov D.B., Matrasulov D.U., Sobirov Z.A., Avazbaev S.K., Karpova O.V. Time-dependent quantum circular billiard. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(2):224-243. https://doi.org/10.17586/2220-8054-2015-6-2-224-243
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