Spectral duality for planar billiards

DOI10.1007/BF02108330zbMath0834.35096arXivchao-dyn/9405001OpenAlexW1994926960MaRDI QIDQ1894881

Jean-Pierre Eckmann, Claude-Alain Pillet

Publication date: 26 July 1995

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/chao-dyn/9405001

zbMATH Keywords

eigenvalues\(S\)-matrixDirichlet Laplacian

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) (S)-matrix theory, etc. in quantum theory (81U20)

Related Items (15)

Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces ⋮ Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions ⋮ The flexibility in choosing distinct Green’s functions for the boundary wall method: waveguides and billiards ⋮ A relative trace formula for obstacle scattering ⋮ Uniqueness in Inverse Scattering Problems with Phaseless Far-Field Data at a Fixed Frequency ⋮ Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues ⋮ Inside-outside duality for a class of modified transmission eigenvalues ⋮ A sharp lower bound for a resonance-counting function in even dimensions ⋮ Eigenstates and scattering solutions for billiard problems: a boundary wall approach ⋮ Equidistribution of phase shifts in obstacle scattering ⋮ Asymptotic completeness and S-matrix for singular perturbations ⋮ Unnamed Item ⋮ Inside–outside duality with artificial backgrounds ⋮ Time delay ⋮ Inside-Outside Duality and the Determination of Electromagnetic Interior Transmission Eigenvalues

Cites Work

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• Chaos in classical and quantum mechanics
• Scattering from a square obstacle
• Asymptotic behalrior of the scattering phase for exterior domains
• Semiclassical quantization of chaotic billiards: a scattering theory approach
• Elliptic Partial Differential Equations of Second Order
• A scattering approach to the quantization of billiards— The inside–outside duality
• Persistent current flux correlations calculated by quantum chaology

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