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Weyl series for Aharonov-Bohm billiards

Record type: Article

Following a conjecture of Berry and Howls (1994) concerning the geometric information contained within the high orders of Weyl series, we examine such series for the average spectral properties of two- and three-dimensional quantum ball billiards threaded by a single flux line at the centre. We adapt a Mellin-based scheme of Bordag et al (1996) to generate the Weyl series. It is shown that for a circular billiard, only a single Weyl series term is changed and thus the flux line only induces a simple constant shift in the average properties of the spectrum, although the fluctuations about this average will still be flux dependent. This implies that the late terms in the expansion are dominated by the diametrical periodic orbit of the unfluxed circle, rather than the shorter diffractive orbits encountering both the billiard boundary and the flux line. For a spherical billiard with flux the late terms suffer modifications which can be linked to diffractive orbits. The origins of the differences between the structure of the series are traced to the interaction of the geometry and symmetry breaking.

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Citation

Howls, C.J. (2001) Weyl series for Aharonov-Bohm billiards Journal of Physics A: Mathematical and General, 34, pp. 7811-7831. (doi:10.1088/0305-4470/34/38/308).

More information

Published date: 2001
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29212
URI: http://eprints.soton.ac.uk/id/eprint/29212
ISSN: 0305-4470
PURE UUID: 2b60d023-cf4b-41a8-8c43-d8fbaca6fc99
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

Catalogue record

Date deposited: 11 May 2006
Last modified: 17 Jul 2017 15:58

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