Hearing shapes of drums: Mathematical and physical aspects of isospectrality
Abstract
In a celebrated paper “Can one hear the shape of a drum?” M. Kac [Am. Math. Monthly 73, 1 (1966)]10.2307/2313748 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.
 Publication:

Reviews of Modern Physics
 Pub Date:
 July 2010
 DOI:
 10.1103/RevModPhys.82.2213
 arXiv:
 arXiv:1101.1239
 Bibcode:
 2010RvMP...82.2213G
 Keywords:

 03.65.Ge;
 05.45.a;
 Solutions of wave equations: bound states;
 Nonlinear dynamics and chaos;
 Mathematical Physics;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 42 pages, 60 figures