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Relativistic kicked rotor.

D U Matrasulov1, G M Milibaeva, U R Salomov

  • 1Heat Physics Department of the Uzbek Academy of Sciences, 28 Katartal St., 700135 Tashkent, Uzbekistan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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Transport properties of the relativistic kicked rotor differ between classical and quantum mechanics. Quantum suppression transitions to classical agreement in the relativistic regime, with no quantum resonances observed.

Area of Science:

  • Physics
  • Quantum Mechanics
  • Relativistic Dynamics

Background:

  • The periodically kicked rotor is a standard model for studying dynamical chaos.
  • Nonrelativistic quantum mechanics exhibits quantum suppression of chaos in this model.
  • Relativistic effects on chaotic systems are not fully understood.

Purpose of the Study:

  • To investigate and contrast transport properties in the relativistic kicked rotor under classical and quantum dynamics.
  • To analyze the transition from nonrelativistic quantum suppression to relativistic quantum-classical agreement.
  • To explore the phenomenon of quantum resonances in the relativistic regime.

Main Methods:

  • Solving the Dirac equation for the quantum rotor with a time-periodic delta-function potential.

Related Experiment Videos

  • Developing a relativistic quantum mapping to describe wave function evolution.
  • Comparing classical and quantum mechanical transport properties.

    • Main Results:

    • Observed a transition from quantum suppression to agreement between quantum and classical analyses in the relativistic regime.
    • Demonstrated the absence of quantum resonances in the relativistic kicked rotor model.
    • Characterized the unique transport properties arising from relativistic quantum dynamics.

    Conclusions:

    • Relativistic quantum mechanics significantly alters the transport properties compared to its nonrelativistic counterpart.
    • The relativistic regime unifies classical and quantum descriptions of chaos in the kicked rotor.
    • Quantum resonances, prevalent in nonrelativistic systems, do not manifest in the relativistic kicked rotor.