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Quantum-to-classical transition in a system with mixed classical dynamics.

Fabricio Toscano1, Diego A Wisniacki

  • 1Fundação Centro de Ciências e Educação Superior a Distância do Estado do Rio de Janeiro, 20943-001 Rio de Janeiro, RJ, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
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Decoherence governs the quantum-classical transition in kicked harmonic oscillators. A universal relation links classical and quantum distributions across dynamics, applicable in the semiclassical limit.

Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • The kicked harmonic oscillator exhibits complex dynamics, transitioning from regular to chaotic behavior based on kick amplitude.
  • Understanding the quantum-classical transition is a fundamental challenge in physics.

Purpose of the Study:

  • To investigate the role of decoherence in the quantum-classical transition of the kicked harmonic oscillator.
  • To establish a relationship between classical and quantum phase space distributions in various dynamical regimes.

Main Methods:

  • Analysis of the kicked harmonic oscillator model.
  • Introduction of noise to study decoherence effects.
  • Derivation of a parameter (chi) relating quantum and classical distributions.

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Main Results:

  • A proportional relationship was found between classical and quantum phase space distributions for regular and mixed dynamics.
  • This relationship is governed by chi = K * (Planck's eff)^2 / (4 * D^(3/2)).
  • The relation holds when chi < 1, achievable in the semiclassical regime regardless of noise strength.

Conclusions:

  • Decoherence plays a crucial role in bridging classical and quantum behaviors.
  • The findings extend previous studies on chaotic regimes to include regular and mixed dynamics.
  • A universal parameter (chi) characterizes the quantum-classical correspondence in this system.