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Diffractive orbits in isospectral billiards

O Giraud

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Isospectral domains are non-isometric regions of space for which the spectra of the Laplace–Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length spectrum, that is the set of the lengths of all periodic trajectories, coincides as well. However there is no one-to-one correspondence between the diffractive trajectories. It will be shown here how the diffractive contributions to the Green functions match nevertheless in a 'one-to-three' correspondence.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.30.Sa Functional analysis

03.65.Ge Solutions of wave equations: bound states

02.70.Hm Spectral methods

MSC

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

37D50 Hyperbolic systems with singularities (billiards, etc.)

Subjects

Mathematical physics

Computational physics

Quantum information and quantum mechanics

Statistical physics and nonlinear systems

Dates

Issue 7 (20 February 2004)

Received 3 November 2003

Published 4 February 2004



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