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Spectral duality for planar billiards

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Published in Communications in Mathematical Physics. 1995, vol. 170, no. 2, p. 283-313
Abstract For a bounded open domain Ω with connected complement inR2 and piecewise smooth boundary, we consider the Dirichlet Laplacian-ΔΩ on Ω and the S-matrix on the complementΩc. We show that the on-shell S-matricesSk have eigenvalues converging to 1 ask↑k0 exactly when--ΔΩ has an eigenvalue at energyk02. This includes multiplicities, and proves a weak form of “transparency” atk=k0. We also show that stronger forms of transparency, such asSk0 having an eigenvalue 1 are not expected to hold in general.
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ECKMANN, Jean-Pierre, PILLET, Claude-Alain. Spectral duality for planar billiards. In: Communications in Mathematical Physics, 1995, vol. 170, n° 2, p. 283-313. https://archive-ouverte.unige.ch/unige:92358

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Deposited on : 2017-03-06

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