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Diffusive-ballistic crossover in 1D quantum walks.

Daniel K Wójcik1, J R Dorfman

  • 1Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. danek@cns.physics.gatech.edu

Physical Review Letters
|July 15, 2003
PubMed
Summary
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Particle transport in quantum multibaker maps shows ballistic motion at long times but diffusive behavior in the semiclassical limit. This crossover is predicted by random matrix theory and linked to classical chaos.

Area of Science:

  • Quantum chaos
  • Quantum statistical mechanics
  • Condensed matter physics

Background:

  • Particle transport in quantum systems is crucial for understanding phenomena from quantum computation to condensed matter physics.
  • The quantum multibaker map serves as a model system for studying quantum chaos and transport properties.

Purpose of the Study:

  • To investigate particle transport dynamics in a uniform quantum multibaker map.
  • To analyze the behavior of mean square displacement in both long-time and semiclassical limits.
  • To explore the connection between classical chaos and quantum transport.

Main Methods:

  • Analysis of equilibrium mean square displacement.
  • Application of random matrix theory for analytical predictions.

Related Experiment Videos

  • Examination of the semiclassical limit.

    • Main Results:

    • Particle transport is generically ballistic in the long-time limit for any fixed Planck's constant.
    • The semiclassical limit exhibits diffusive behavior for fixed times.
    • A crossover from diffusive to ballistic motion is observed, with crossover time dependent on Planck's constant.

    Conclusions:

    • Random matrix theory accurately predicts the mean square displacement and crossover behavior.
    • Classically chaotic dynamics within cells is a sufficient condition for diffusion in the semiclassical limit for similar 1D quantum random walks.
    • The studied systems generalize known quantum random walks and have potential applications in quantum computation.