Hearing shapes of drums – mathematical and physical aspects of isospectrality

O. Giraud 1, K. Thas 2

Reviews of Modern Physics 82 (2010) 2213-2255

In a celebrated paper  »Can one hear the shape of a drum? » M. Kac [Amer. Math. Monthly 73, 1 (1966)] asked his famous question about the existence of nonisometric billiards having the same spectrum of the Laplacian. This question was eventually answered positively in 1992 by the construction of noncongruent planar isospectral pairs. This review highlights mathematical and physical aspects of isospectrality.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI – Paris Sud
  • 2. Department of Pure Mathematics and Computer Algebra,
    Ghent University
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