'Can one hear the shape of a drum?': Revisited

Y. Okada, A. Shudo, S. Tasaki, T. Harayama

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

A famous inverse problem posed by M Kac 'Can one hear the shape of a drum?' is concerned with isospectrality of drums or planer billiards, and the first counter example was constructed by Gordon, Webb and Wolpert (1992 Invent. Math. 110 1). Here we present pieces of numerical evidence showing that 'One can distinguish isospectral drums by measuring the scattering poles of exterior Neumann problems'. This is based on the observation that the Fredholm determinant appearing in the boundary element method admits a factorization into interior and exterior parts.

Original languageEnglish
Pages (from-to)L163-L170
JournalJournal of Physics A: Mathematical and General
Volume38
Issue number9
DOIs
Publication statusPublished - 2005 Mar 4
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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