Asymptotic-boundary-layer method for unstable trajectories: Semiclassical expansions for individual scar wave functions

A. Vagov, H. Schomerus, and V. V. Zalipaev
Phys. Rev. E 80, 056202 – Published 3 November 2009

Abstract

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions 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.

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  • Received 6 July 2009

DOI:https://doi.org/10.1103/PhysRevE.80.056202

©2009 American Physical Society

Authors & Affiliations

A. Vagov1,2, H. Schomerus2, and V. V. Zalipaev3,4

  • 1Institut für Theoretische Physik III, Bayreuth Universität, Bayreuth 95440, Germany
  • 2Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
  • 3Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
  • 4Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

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Issue

Vol. 80, Iss. 5 — November 2009

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