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Semiclassical approximation for a nonlinear oscillator with dissipation.

A Iomin1

  • 1Department of Physics, Technion, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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This study introduces an S-matrix method to analyze chaotic nonlinear oscillators with dissipation. It reveals the quantum-classical crossover and derives the breaking time, crucial for dissipative systems.

Area of Science:

  • * Physics, specifically quantum mechanics and nonlinear dynamics.
  • * Focus on chaotic systems and their quantum-classical behavior.

Background:

  • * Understanding chaotic dynamics in nonlinear oscillators is complex.
  • * Dissipation introduces unique challenges to quantum-classical transitions.

Purpose of the Study:

  • * To develop an S-matrix approach for dissipative chaotic nonlinear oscillators.
  • * To investigate the quantum-classical crossover in such systems.
  • * To determine the breaking time (Ehrenfest time) for dissipative systems.

Main Methods:

  • * Utilized an S-matrix approach.
  • * Employed semiclassical expansion for the S-matrix.
  • * Analyzed correlation functions of S-matrix elements.

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Main Results:

  • * Developed a novel S-matrix method for dissipative chaotic systems.
  • * Obtained an analytical expression for the breaking time.
  • * Studied the quantum-classical crossover dynamics.

Conclusions:

  • * The S-matrix approach provides a framework for studying quantum-classical transitions in dissipative chaotic systems.
  • * The derived breaking time is a key parameter for understanding system behavior.
  • * Further analysis of S-matrix element correlations offers insights into system dynamics.