Quantum-to-Classical Crossover of Quasibound States in Open Quantum Systems

2004/06/30 by Henning Schomerus, J. Tworzydło, Jakub Tworzydlo · 3 citations
Chemistry · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Molecular spectroscopy and chirality #Quantum chaos and dynamical systems #cond-mat.mes-hall #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physrevlett.93.154102

published as Phys. Rev. Lett. 93, 154102 (2004) · 4 pages, 2 figures, corrected misprint in Eqs (6,7), minor revisions

arxiv created 2004/09/01 · openalex publication_date 2004/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasibound states is smaller than the classical time of flight. The remaining long-lived quasibound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W.T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically for a model system, the open kicked rotator.

Citations

• Quantum-to-classical crossover of mesoscopic conductance fluctuations
• Noiseless scattering states in a chaotic cavity
• Truncations of random unitary matrices
• Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator
• Random-matrix theory of quantum transport
• Dynamical model for the quantum-to-classical crossover of shot noise
• Fractal Weyl Laws for Chaotic Open Systems
• Adiabatic Quantization of Andreev Quantum Billiard Levels
• Quantum Andreev Map: A Paradigm of Quantum Chaos in Superconductivity

Cited by

• Quantum-to-classical correspondence in open chaotic systems
• Fractal Weyl law for quantum fractal eigenstates
• Semiclassical Structure of Chaotic Resonance Eigenfunctions