An efficient Fredholm method for the calculation of highly excited states of billiards

Hakan E. Türeci, Harald G.L. Schwefel

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A numerically efficient Fredholm formulation of the billiard problem is presented. The standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first. We next reformulate the singularity condition in terms of a flow in the space of an auxiliary one-parameter family of eigenproblems and argue that the eigenvalues and eigenfunctions are analytic functions within a certain domain. Based on this analytic behavior, we present a numerical algorithm to compute a range of billiard eigenvalues and associated eigenvectors by only two diagonalizations.

Original languageEnglish (US)
Pages (from-to)13869-13882
Number of pages14
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number46
DOIs
StatePublished - Nov 16 2007

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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