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Nodal domains of the equilateral triangle billiard

Samajdar, Rhine and Jain, Sudhir R (2014) Nodal domains of the equilateral triangle billiard. In: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 47 (19).

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Official URL: http://dx.doi.org/10.1088/1751-8113/47/19/195101


We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

Item Type: Journal Article
Additional Information: copyright for this article belongs toIOP PUBLISHING LTD, England.
Keywords: Schrodinger equation; non-separable systems; quantum chaos; billiards
Department/Centre: UG Programme
Date Deposited: 14 Jun 2014 05:06
Last Modified: 14 Jun 2014 05:06
URI: http://eprints.iisc.ac.in/id/eprint/49247

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