0000000000512878
AUTHOR
E. De Prunelé
showing 2 related works from this author
Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk…
2019
A deformation of a disk D of radius r is described as follows: Let two disks D1 and D2 have the same radius r, and let the distance between the two disk centers be 2a, 0 ≤ a ≤ r. The deformation transforms D into the intersection D1 ∩ D2. This deformation is parametrized by e = a/r. For e = 0, there is no deformation, and the deformation starts when e, starting from 0, increases, transforming the disk into a lens. Analytic results are obtained for the eigenvalues of Helmholtz equation with zero Dirichlet boundary condition to the lowest order in e for this deformation. These analytic results are obtained via a Hamiltonian method for solving the Helmholtz equation with zero Dirichlet boundar…
Two-dimensional quantum scattering by non-isotropic interactions localized on a circle, applications to open billiards
2018
Two-dimensional quantum scattering by isotropic and non-isotropic interactions localized on a circle is considered. The expansion of the interaction on the circle in a Fourier series allows us to express basic objects of scattering theory (resolvent, T operator, differential cross length, cross length, and cross length averaged over all orientations of the incident particle), in terms of operations on matrices. For numerical applications, these matrices are truncated to a given order. If the interaction is isotropic, this general formulation reduces to the usual one, and the resonances in the isotropic cases are studied because they allow us to interpret resonances in some non-isotropic cas…