2003/06/30 by Tomaž Prosen, Tomaz Prosen, Marko Znidaric +1
Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Integrable system #Mathematical physics #Operator (biology) #Perturbation (astronomy) #Physics #Planck constant #Quantum #Quantum chaos and dynamical systems #Quantum dynamics #Quantum fluctuation #Quantum mechanics #Quantum, superfluid, helium dynamics #Semiclassical physics #Statistical physics #nlin.CD #nlin.SI #quant-ph
paper · pdf · doi:10.1088/1367-2630/5/1/109
published as New Journal of Physics 5 (2003) 109 · 32 pages, 8 figures (1 color); minor typos corrected, published version; see also movies at http://chaos.fiz.uni-lj.si/papers/freeze
arxiv created 2003/08/19 · openalex publication_date 2003/08/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss quantum fidelity decay of classically regular dynamics, in particular for an important special case of a vanishing time-averaged perturbation operator, i.e. vanishing expectation values of the perturbation in the eigenbasis of unperturbed dynamics. A complete semiclassical picture of this situation is derived in which we show that the quantum fidelity of individual coherent initial states exhibits three different regimes in time: (i) first it follows the corresponding classical fidelity up to time , (ii) then it freezes on a plateau of constant value, (iii) and after a timescale it exhibits fast ballistic decay as where is a strength of perturbation. All the constants are computed in terms of classical dynamics for sufficiently small effective value of the Planck constant. A similar picture is worked out also for general initial states, and specifically for random initial states, where , and . This prolonged stability of quantum dynamics in the case of a vanishing time-averaged perturbation could prove to be useful in designing quantum devices. Theoretical results are verified by numerical experiments on the quantized integrable kicked top.