Publication result detail
Optical simulation of quantum mechanics on the Mobius strip, Klein's bottle and other manifolds, and Talbot effect
BĚLÍN, J.; TYC, T.; HORSLEY, S.
Original Title
Optical simulation of quantum mechanics on the Mobius strip, Klein's bottle and other manifolds, and Talbot effect
English Title
Optical simulation of quantum mechanics on the Mobius strip, Klein's bottle and other manifolds, and Talbot effect
Type
WoS Article
Original Abstract
We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Mobius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.
English abstract
We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Mobius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.
Keywords
curved spaces; quantum revivals; Talbot effect; topology; orbifolds
Key words in English
curved spaces; quantum revivals; Talbot effect; topology; orbifolds
Authors
BĚLÍN, J.; TYC, T.; HORSLEY, S.
RIV year
2022
Released
01.03.2021
Publisher
IOP Publishing
Location
BRISTOL
ISBN
1367-2630
Periodical
NEW JOURNAL OF PHYSICS
Volume
23
Number
3
State
United Kingdom of Great Britain and Northern Ireland
Pages from
1
Pages to
11
Pages count
11
URL
Full text in the Digital Library
BibTex
@article{BUT173122,
author="Jakub {Bělín} and Tomáš {Tyc} and Simon A. R. {Horsley}",
title="Optical simulation of quantum mechanics on the Mobius strip, Klein's bottle and other manifolds, and Talbot effect",
journal="NEW JOURNAL OF PHYSICS",
year="2021",
volume="23",
number="3",
pages="1--11",
doi="10.1088/1367-2630/abe445",
issn="1367-2630",
url="https://iopscience.iop.org/article/10.1088/1367-2630/abe445"
}Documents
Responsibility: Ing. Marek Strakoš