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Classical dynamical localization.

Italo Guarneri1, Giulio Casati2, Volker Karle3

  • 1Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy.

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Summary
This summary is machine-generated.

Classical models exhibit quasilocalization and quadratic energy growth, mimicking quantum kicked rotor dynamics. This suggests localization and resonances may not solely depend on quantum coherence.

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Area of Science:

  • Classical mechanics
  • Quantum chaos
  • Statistical physics

Background:

  • The quantum kicked rotor model exhibits dynamical localization and quantum resonances.
  • These phenomena are typically attributed to quantum coherence effects.

Purpose of the Study:

  • To investigate classical models that mimic quantum kicked rotor dynamics.
  • To explore the role of classical mechanics in phenomena like dynamical localization and quantum resonances.

Main Methods:

  • Considered classical kicked rotor models with piecewise linear potentials.
  • Analyzed dynamics based on the arithmetic nature of momentum change.
  • Developed a heuristic explanation mapping the quantum kicked rotor to a disordered tight-binding model.

Main Results:

  • Classical models displayed quasilocalization of momentum or quadratic energy growth.
  • These classical dynamics mirrored key features of the quantum kicked rotor.
  • A classical phase space argument provided a heuristic explanation for the observed phenomena.

Conclusions:

  • Dynamical localization and quantum resonances can emerge from purely classical dynamics.
  • These findings challenge the notion that quantum coherence is essential for such phenomena.
  • Classical models offer valuable insights into quantum chaotic systems.