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Dynamical localization in quasiperiodic driven systems.

G Abal1, R Donangelo, A Romanelli

  • 1Instituto de Física, Facultad de Ingeniería, Universidad de la República, CC 30, C. P. 11000, Montevideo, Uruguay. abal@fing.edu.uy

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
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Dynamical localization (DL) in driven quantum systems depends on Hamiltonian time dependence. Impulsive terms destroy DL, while smooth driving functions preserve it longer, with localization time scaling as sigma(-2) with pulse duration.

Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Nonlinear dynamics

Background:

  • Dynamical localization (DL) is a phenomenon in driven quantum systems where particles become spatially localized despite continuous driving.
  • The time dependence of the Hamiltonian plays a crucial role in the emergence and stability of DL.

Purpose of the Study:

  • To investigate the influence of the Hamiltonian's time dependence on dynamical localization in quantum systems driven by two incommensurate frequencies.
  • To analyze how different forms of driving functions (impulsive vs. smooth) affect DL.
  • To explore the transition from localized to delocalized dynamics in intermediate driving cases.

Main Methods:

  • Numerical simulations of driven quantum systems.
  • Analytical considerations to estimate critical parameters.

Related Experiment Videos

  • Analysis of the frequency spectrum of the dynamical response.

    • Main Results:

    • Permanent destruction of DL when both driving frequencies are associated with impulsive terms, leading to decoherent-like evolution.
    • Persistence of DL for smooth driving functions, albeit on extended time scales.
    • Localization time scales as sigma(-2) as the impulsive limit (sigma-->0) is approached for pulsed driving.
    • Observation of a transition from localized to delocalized dynamics in intermediate cases with one impulsive term, with an estimated critical strength parameter.

    Conclusions:

    • The time dependence of the Hamiltonian is a critical factor governing DL in driven quantum systems.
    • The nature of the driving function dictates the presence, duration, and characteristics of DL.
    • The frequency spectrum provides insights into the system's dynamical behavior across different regimes.