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Related Experiment Videos

Quantum breaking time near classical equilibrium points.

Fabrizio Cametti1, Carlo Presilla

  • 1Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale A. Moro 2, Roma 00185, Italy.

Physical Review Letters
|July 30, 2002
PubMed
Summary
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Quantum-classical correspondence breaks down at the Ehrenfest time. This time diverges logarithmically for exponentially unstable equilibrium points and follows a power law otherwise, depending on potential degree.

Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • Quantum-classical correspondence describes how quantum mechanics approaches classical mechanics at larger scales.
  • The breakdown of this correspondence is linked to the Ehrenfest time, a critical timescale.
  • Understanding this breakdown is crucial for quantum chaos studies.

Purpose of the Study:

  • To investigate the behavior of the Ehrenfest time in one-dimensional systems.
  • To determine how the nature of the classical equilibrium point affects the quantum breaking time.
  • To analyze the relationship between Planck's constant and the Ehrenfest time.

Main Methods:

  • Studied one-dimensional systems with single- and double-well polynomial potentials.
  • Analyzed the evolution of quantum distributions around classical equilibrium points.

Related Experiment Videos

  • Investigated the dependence of Ehrenfest time on the stability of equilibrium points and Planck's constant.

    • Main Results:

    • The Ehrenfest time diverges logarithmically with the inverse of Planck's constant for exponentially unstable equilibrium points.
    • For other cases, the Ehrenfest time exhibits a power-law divergence.
    • The exponent in the power-law divergence is determined by the degree of the potential near the equilibrium point.

    Conclusions:

    • The stability of classical equilibrium points fundamentally dictates the nature of quantum-classical correspondence breakdown.
    • Ehrenfest time provides a critical measure for quantum chaos, with distinct behaviors for stable and unstable systems.
    • The findings offer insights into quantum decoherence and the transition from quantum to classical dynamics.