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Spectral duality for planar billiards (1995)

Eckmann, Jean-Pierre ; Pillet, Claude-Alain

Springer

Communications in mathematical physics 170 (1995), S. 283-313

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract For a bounded open domain Ω with connected complement inR 2 and piecewise smooth boundary, we consider the Dirichlet Laplacian-Δ Ω on Ω and the S-matrix on the complementΩ c . We show that the on-shell S-matricesS k have eigenvalues converging to 1 ask↑k 0 exactly when--Δ Ω has an eigenvalue at energyk 0 2 . This includes multiplicities, and proves a weak form of “transparency” atk=k 0. We also show that stronger forms of transparency, such asS k 0 having an eigenvalue 1 are not expected to hold in general.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02108330

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