Hearing shapes of drums - mathematical and physical aspects of isospectrality

Details Hearing shapes of drums - mathematical and physical aspects of isospectrality Hearing shapes of drums - mathematical and physical aspects of isospectrality

2011-01-06

arxiv.org/abs/1101.1239v1

Rev. Mod. Phys. 82, 2213 (2010)

Physics

Mathematical Physics

42 pages, 60 figures

Scientific paper

10.1103/RevModPhys.82.2213

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.

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