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

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• 作者：Naren Manjunath^a ; Rhine Samajdar^a ; Sudhir R. Jain^b ; ^{srjain@barc.gov.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Integrable billiard ; Nodal domain ; Quantum chaos
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：372
• 期：Complete
• 页码：68-73
• 全文大小：1004 K

文摘

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.