Computing Maass cusp form on general hyperbolic torus

The bound states of a quantum mechanical system on a punctured hyperbolic torus are described by Maass cusp forms, which are eigenfunctions of the hyperbolic Laplace-Beltrami operator vanishing at infinity. In a recent work by Chan et al. (2013), the computation of Maass cusp forms makes use of the...

Full description

Saved in:
Bibliographic Details
Main Authors: Shamsuddin, Nor Syazana, Zainuddin, Hishamuddin, Chan, Kar Tim
Format: Conference or Workshop Item
Language:English
Published: AIP Publishing 2016
Online Access:http://psasir.upm.edu.my/id/eprint/57260/1/Computing%20Maass%20cusp%20form%20on%20general%20hyperbolic%20torus.pdf
http://psasir.upm.edu.my/id/eprint/57260/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.57260
record_format eprints
spelling my.upm.eprints.572602017-09-26T03:48:28Z http://psasir.upm.edu.my/id/eprint/57260/ Computing Maass cusp form on general hyperbolic torus Shamsuddin, Nor Syazana Zainuddin, Hishamuddin Chan, Kar Tim The bound states of a quantum mechanical system on a punctured hyperbolic torus are described by Maass cusp forms, which are eigenfunctions of the hyperbolic Laplace-Beltrami operator vanishing at infinity. In a recent work by Chan et al. (2013), the computation of Maass cusp forms makes use of the symmetric fundamental domain for the hyperbolic torus. As a result, the Maass cusp forms then are divided into odd and even classes. It is of interest to consider the case when no symmetry is assumed. This requires the expansion of Maass cusp form in its complex Fourier form. In this paper, we show the available algorithm can be extended to employ directly the complex Fourier expansion using Mathematica. We were able to reproduce the results of Chan et al, on the symmetric hyperbolic torus but now with the capability of applying the algorithm even for the case of asymmetric hyperbolic torus. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57260/1/Computing%20Maass%20cusp%20form%20on%20general%20hyperbolic%20torus.pdf Shamsuddin, Nor Syazana and Zainuddin, Hishamuddin and Chan, Kar Tim (2016) Computing Maass cusp form on general hyperbolic torus. In: 2nd International Conference and Workshop on Mathematical Analysis (ICWOMA 2016), 2-4 Aug. 2016, Langkawi, Malaysia. (pp. 1-8). 10.1063/1.4972158
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description The bound states of a quantum mechanical system on a punctured hyperbolic torus are described by Maass cusp forms, which are eigenfunctions of the hyperbolic Laplace-Beltrami operator vanishing at infinity. In a recent work by Chan et al. (2013), the computation of Maass cusp forms makes use of the symmetric fundamental domain for the hyperbolic torus. As a result, the Maass cusp forms then are divided into odd and even classes. It is of interest to consider the case when no symmetry is assumed. This requires the expansion of Maass cusp form in its complex Fourier form. In this paper, we show the available algorithm can be extended to employ directly the complex Fourier expansion using Mathematica. We were able to reproduce the results of Chan et al, on the symmetric hyperbolic torus but now with the capability of applying the algorithm even for the case of asymmetric hyperbolic torus.
format Conference or Workshop Item
author Shamsuddin, Nor Syazana
Zainuddin, Hishamuddin
Chan, Kar Tim
spellingShingle Shamsuddin, Nor Syazana
Zainuddin, Hishamuddin
Chan, Kar Tim
Computing Maass cusp form on general hyperbolic torus
author_facet Shamsuddin, Nor Syazana
Zainuddin, Hishamuddin
Chan, Kar Tim
author_sort Shamsuddin, Nor Syazana
title Computing Maass cusp form on general hyperbolic torus
title_short Computing Maass cusp form on general hyperbolic torus
title_full Computing Maass cusp form on general hyperbolic torus
title_fullStr Computing Maass cusp form on general hyperbolic torus
title_full_unstemmed Computing Maass cusp form on general hyperbolic torus
title_sort computing maass cusp form on general hyperbolic torus
publisher AIP Publishing
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/57260/1/Computing%20Maass%20cusp%20form%20on%20general%20hyperbolic%20torus.pdf
http://psasir.upm.edu.my/id/eprint/57260/
_version_ 1643836434620088320
score 13.209306