Asymptotic boundary layer method for unstable trajectories: Semiclassics for individual scar wavefunctions

Abstract

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wavefunctions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

9 pages, 2 figures

References in corpus (4)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Quantum-to-classical correspondence in open chaotic systems
• Quantum chaotic resonances from short periodic orbits

Cited by in corpus (7)

• Two-band superconductors: Extended Ginzburg-Landau formalism by a systematic expansion in small deviation from the critical temperature
• Regular Oscillation Sub-spectrum of Rapidly Rotating Stars
• Regular modes in rotating stars
• Using basis sets of scar functions
• The short periodic orbit method for excited chaotic eigenfunctions
• Semiclassical basis sets for the computation of molecular vibrational states
• Semiclassical matrix elements for a chaotic propagator in the Scar functions basis