Resolving isospectral 'drums' by counting nodal domains
(2005) In Journal of Physics A: Mathematical and General 38(41). p.8921-8933- Abstract
- Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace-Beltrami operators for pairs of flat tori in R-n with n >= 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions-where a four-parameter family of isospectral pairs is known-we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus one can count the shape of a drum (if it is... (More)
- Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace-Beltrami operators for pairs of flat tori in R-n with n >= 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions-where a four-parameter family of isospectral pairs is known-we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus one can count the shape of a drum (if it is designed as a flat torus in four dimensions). (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/213834
- author
- Gnutzmann, S ; Smilansky, U and Søndergaard, Niels LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics A: Mathematical and General
- volume
- 38
- issue
- 41
- pages
- 8921 - 8933
- publisher
- IOP Publishing
- external identifiers
-
- wos:000233112500008
- scopus:25844479881
- ISSN
- 0305-4470
- DOI
- 10.1088/0305-4470/38/41/006
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Physics (Faculty of Technology) (011040002)
- id
- d6c7963c-7c9a-4d4f-9bbd-3bd313fb278d (old id 213834)
- date added to LUP
- 2016-04-01 16:17:32
- date last changed
- 2022-03-30 06:53:28
@article{d6c7963c-7c9a-4d4f-9bbd-3bd313fb278d,
abstract = {{Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace-Beltrami operators for pairs of flat tori in R-n with n >= 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions-where a four-parameter family of isospectral pairs is known-we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus one can count the shape of a drum (if it is designed as a flat torus in four dimensions).}},
author = {{Gnutzmann, S and Smilansky, U and Søndergaard, Niels}},
issn = {{0305-4470}},
language = {{eng}},
number = {{41}},
pages = {{8921--8933}},
publisher = {{IOP Publishing}},
series = {{Journal of Physics A: Mathematical and General}},
title = {{Resolving isospectral 'drums' by counting nodal domains}},
url = {{http://dx.doi.org/10.1088/0305-4470/38/41/006}},
doi = {{10.1088/0305-4470/38/41/006}},
volume = {{38}},
year = {{2005}},
}