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Quantum diffusion in the Harper model under polychromatic time-perturbation.

Hiroaki S Yamada1, Kensuke S Ikeda2

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Summary
This summary is machine-generated.

Adding multiple frequencies to the Harper model transforms localized states into quantum diffusive states. This transition to diffusion occurs as perturbation strength increases for three or more incommensurate frequencies.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics

Background:

  • The Harper model describes quantum dynamics in a magnetic field.
  • Its states can be localized, diffusive, or ballistic, influenced by potential strength (V).

Purpose of the Study:

  • To investigate the effect of time-dependent harmonic perturbations on Harper model dynamics.
  • To determine the conditions under which different quantum states transition to diffusive states.

Main Methods:

  • Applying time-dependent harmonic perturbations with M incommensurate frequencies to the Harper model.
  • Analyzing the resulting quantum dynamics and state transitions.
  • Mapping the phase diagram in the (ε,V) parameter space.

Main Results:

  • All Harper model states transition to quantum diffusive states as perturbation strength (ε) increases for M≥3.
  • The transition schemes and diffusion behaviors are dependent on ε and V.
  • A phase diagram illustrating these transitions is presented.

Conclusions:

  • Time-dependent perturbations with sufficient incommensurate frequencies can drive localization-free quantum diffusion.
  • The Harper model's dynamics are highly sensitive to external time-dependent perturbations.