Scar intensity statistics in the position representation

2005/10/18 by K. Damborsky, L. Kaplan
Physics and Astronomy · #Chaos control and synchronization #Quantum chaos and dynamical systems #Theoretical and Computational Physics #nlin.CD

paper · pdf · doi:10.1103/physreve.72.066204

published as Phys. Rev. E 72, 066204 (2005) · To appear in Phys. Rev. E, 10 pages, including 4 figures

arxiv created 2005/10/18 · openalex publication_date 2005/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain general predictions for the distribution of wave function intensities in position space on the periodic orbits of chaotic ballistic systems. The expressions depend on effective system size , instability exponent of the periodic orbit, and proximity to a focal point of the orbit. Limiting expressions are obtained that include the asymptotic probability distribution of rare high-intensity events and a perturbative formula valid in the limit of weak scarring. For finite system sizes, a single scaling lambdaN variable describes deviations from the semiclassical N--> infinity limit.

Citations

• Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• A universal instability of many-dimensional oscillator systems