Fredholm methods for billiard eigenfunctions in the coherent state representation

Abstract

We obtain a semiclassical expression for the projector onto eigenfunctions by means of the Fredholm theory. We express the projector in the coherent state basis, thus obtaining the semiclassical Husimi representation of the stadium eigenfunctions, which is written in terms of classical invariants: periodic points, their monodromy matrices and Maslov indices.

12 pages, 10 figures. Submitted to Phys. Rev. E. Comments or questions to [email protected]

References in corpus (2)

• Linear and Nonlinear Theory of Eigenfunction Scars
• Quantitative study of scars in the boundary section of the stadium billiard

Cited by in corpus (4)

• Poincaré Husimi representation of eigenstates in quantum billiards
• An efficient Fredholm method for calculation of highly excited states of billiards
• Wavefunctions, Green's functions and expectation values in terms of spectral determinants
• On resumming periodic orbits in the spectra of integrable systems