Probabilistic description of dissipative chaotic scattering.

We investigate the extent to which the probabilistic properties of chaotic scattering systems with dissipation can be understood from the properties of the dissipation-free system. For large energies, a fully chaotic scattering leads to an exponential decay of the survival probability P(t)∼e^{-κt}, with an escape rate κ that decreases with energy. Dissipation leads to the appearance of different finite-time regimes in P(t).

Defect in the Joint Spectrum of Hydrogen due to Monodromy.

In addition to the well-known case of spherical coordinates, the Schrödinger equation of the hydrogen atom separates in three further coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators. We show that the joint spectrum of the Hamilton operator, the z component of the angular momentum, and an operator involving the z component of the quantum Laplace-Runge-Lenz vector obtained from separation in prolate spheroidal coordinates has quantum monodromy for energies sufficiently close to the ionization threshold.

Nonuniqueness of the phase shift in central scattering due to monodromy.

Scattering at a central potential is completely characterized by the phase shifts which are the differences in phase between outgoing scattered and unscattered partial waves. In this Letter, it is shown that, for 2D scattering at a repulsive central potential, the phase shift cannot be uniquely defined due to a topological obstruction which is similar to monodromy in bound systems.

A two-parameter study of the extent of chaos in a billiard system.

The billiard system of Benettin and Strelcyn [Phys. Rev. A 17, 773-785 (1978)] is generalized to a two-parameter family of different shapes.