Weyl's Wedges

Howls, C.J. and Trasler, S.A. (1998) Weyl's Wedges. Journal of Physics A: Mathematical and General, 31, (8), 1911-1928. (doi:10.1088/0305-4470/31/8/005).


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The semiclassical Weyl series for an arbitrary-angle, zero-potential, circular-wedge quantum billiard with Dirichlet boundary conditions is derived. The goal is to study the effect of non-smooth boundaries on a conjecture of Berry and Howls (1994) concerning the high orders. The dominant behaviour of the late terms is identified, together with correction terms. The factorial-over-power and correction behaviour is found to be in accordance with an extension of the work of Berry and Howls. As might be expected, the only dominant contributions from the polygonal corner are to the `length' and `constant' terms of the Weyl series. The same is not true for the other angles. Surprisingly, only one periodic orbit arising from the wedge geometry affects the Weyl series for arbitrary angle of opening, although there is a subdominant residue from a memory of the circular symmetry. The prefactor of this residue is proportional to . Nevertheless, with one exception, the analytic behaviour of the Weyl series conspires to force the appearance of only the expected wedge periodic orbits in the exponential corrections.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1088/0305-4470/31/8/005
ISSNs: 0305-4470 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 29203
Accepted Date and Publication Date:
Date Deposited: 03 May 2007
Last Modified: 31 Mar 2016 11:54
URI: http://eprints.soton.ac.uk/id/eprint/29203

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