Wavefunction Statistics using Scar States
arXiv:nlin/0304018 · doi:10.1016/S0003-4916(03)00081-2
Abstract
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and provide a natural means of characterising scarring effects in individual wavefunctions as well as their collective statistical properties. In particular, these states may be used to find scarring in regions of the spectrum normally associated with antiscarring and suggest a characterisation of templates for scarred wavefunctions which vary over the spectrum. The results are applied to quantum maps and billiard systems.
31 pages, 11 figures, to appear in Annals of Physics
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Cited by in corpus (7)
- Quasi-Scarred Resonances in a Spiral-Shaped Microcavity
- Scarred Resonances and Steady Probability Distribution in a Chaotic Microcavity
- Poincaré Husimi representation of eigenstates in quantum billiards
- Short periodic orbit approach to resonances and the fractal Weyl law
- Asymptotic boundary layer method for unstable trajectories: Semiclassics for individual scar wavefunctions
- Semiclassical matrix elements for a chaotic propagator in the Scar functions basis
- Scarring in open chaotic systems: The local density of states