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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
Summary

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.

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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.