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Title: A difference-equation formalism for the nodal domains of separable billiards

Abstract

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

Authors:
;  [1];  [2]
  1. Indian Institute of Science, Bangalore 560012 (India)
  2. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)
Publication Date:
OSTI Identifier:
22617371
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CHAOS THEORY; DIRICHLET PROBLEM; EXACT SOLUTIONS; INTEGRAL CALCULUS

Citation Formats

Manjunath, Naren, Samajdar, Rhine, and Jain, Sudhir R., E-mail: srjain@barc.gov.in. A difference-equation formalism for the nodal domains of separable billiards. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.04.014.
Manjunath, Naren, Samajdar, Rhine, & Jain, Sudhir R., E-mail: srjain@barc.gov.in. A difference-equation formalism for the nodal domains of separable billiards. United States. doi:10.1016/J.AOP.2016.04.014.
Manjunath, Naren, Samajdar, Rhine, and Jain, Sudhir R., E-mail: srjain@barc.gov.in. Thu . "A difference-equation formalism for the nodal domains of separable billiards". United States. doi:10.1016/J.AOP.2016.04.014.
@article{osti_22617371,
title = {A difference-equation formalism for the nodal domains of separable billiards},
author = {Manjunath, Naren and Samajdar, Rhine and Jain, Sudhir R., E-mail: srjain@barc.gov.in},
abstractNote = {Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.},
doi = {10.1016/J.AOP.2016.04.014},
journal = {Annals of Physics},
number = ,
volume = 372,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 2016},
month = {Thu Sep 15 00:00:00 EDT 2016}
}