Semiclassical Quantisation Using Diffractive Orbits

Details Semiclassical Quantisation Using Diffractive Orbits Semiclassical Quantisation Using Diffractive Orbits

1995-09-27

arxiv.org/abs/chao-dyn/9509020v1

Phys. Rev. Lett. 76 (1996), p.2605.

Nonlinear Sciences

Chaotic Dynamics

Revtex document. Submitted to PRL. Figures available on request

Scientific paper

10.1103/PhysRevLett.76.2605

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we construct the corresponding zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the diffractive zeta function.

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