2006/05/31 by J. P. Keating, Jonathan P. Keating, Marcel Novaes +5
Physics and Astronomy · #Chaos control and synchronization #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physrevlett.97.150406
published as Phys. Rev. Lett. 97, 150406 (2006) · 4 pages, 4 figures; some minor corrections, some changes in presentation
arxiv created 2006/08/16 · openalex publication_date 2006/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as variant Planck's over 2pi-->0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates [psi(variant Planck's over)] 2pi-->0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker's map, for which the probability density in position space is observed to have self-similarity properties.