2008/07/31 by Valentin V. Sokolov, O. V. Zhirov, Oleg V. Zhirov +2 · 23 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Harmonic oscillator #Isotropy #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Quartic function #Time evolution #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.78.046212
published in Physical Review E 78(4), 046212 (American Physical Society) · 15 pages, 13 figures; the list of references is updated
openalex publication_date 2008/10/21 · arxiv created 2008/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure in its time evolution. This complexity is characterized by the number M(t) of harmonics of the [initially isotropic, i.e., M(0)=0 ] Wigner function, which are generated during quantum evolution for the time t . We show that, in contrast to the classical exponential increase, this number can grow not faster than linearly and then relate this fact with the degree of reversibility of the quantum motion. To explore the reversibility we reverse the quantum evolution at some moment T immediately after applying at this moment an instant perturbation governed by a strength parameter xi . It follows that there exists a critical perturbation strength xic approximately sqrt 2/M(T) below which the initial state is well recovered, whereas reversibility disappears when xi > or approximately xic(T) . In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model.