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Parameter scaling in the decoherent quantum-classical transition for chaotic systems.

Arjendu K Pattanayak1, Bala Sundaram, Benjamin D Greenbaum

  • 1Department of Physics, Carleton College, Northfield, Minnesota 55057, USA.

Physical Review Letters
|February 7, 2003
PubMed
Summary

This study introduces a new composite parameter to unify quantum and classical system transitions. It reveals accurate scaling behavior, suggesting a method for creating universality classes in quantum-classical dynamics.

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • The transition from quantum to classical behavior is influenced by action scale, environmental coupling, and Lyapunov exponent.
  • Understanding this transition is crucial for unifying quantum and classical physics.

Purpose of the Study:

  • To propose a method for measuring the proximity of quantum and classical evolutions.
  • To identify transformations that simplify the multivariate dependence of this proximity into a single composite parameter.

Main Methods:

  • Developed a multivariate function to quantify the difference between quantum and classical system evolutions.
  • Investigated transformations to collapse this function into a composite parameter (zeta).
  • Tested the approach using the quantum Cat Map and Duffing oscillator models.

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Main Results:

  • Demonstrated accurate scaling behavior across a wide parameter range for the tested systems.
  • The proposed composite parameter (zeta) effectively captures the quantum-to-classical transition.
  • The results show consistency with theoretical predictions.

Conclusions:

  • The proposed composite parameter offers a unified approach to studying the quantum-to-classical transition.
  • This framework can be used to establish universality classes for the transition.
  • The findings have implications for understanding complex quantum systems.