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Classical divergence of nonlinear response functions.

Maksym Kryvohuz1, Jianshu Cao

  • 1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|February 21, 2006
PubMed
Summary

Classical mechanics struggles with dynamic perturbation due to time-divergent nonlinear response functions. This divergence persists even with phase-space averaging, impacting quantum-classical correspondence in dynamic response studies.

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Area of Science:

  • Classical mechanics
  • Nonlinear dynamics
  • Quantum-classical correspondence

Background:

  • Dynamic perturbation in classical mechanics presents fundamental challenges.
  • Nonlinear response functions exhibit time divergence, complicating theoretical treatments.

Purpose of the Study:

  • To investigate the nature of time divergence in classical nonlinear response functions.
  • To determine if phase-space averaging can resolve this divergence.
  • To explore implications for quantum-classical correspondence.

Main Methods:

  • Asymptotic decomposition of Fourier integrals.
  • Analysis of systems in regular motions.
  • Theoretical examination of phase-space averaging techniques.

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Main Results:

  • The time divergence of classical nonlinear response functions is characterized.
  • Asymptotic analysis confirms divergence cannot be removed by standard phase-space averaging (e.g., Boltzmann distribution).

Conclusions:

  • The inherent time divergence poses a fundamental limitation for classical dynamic perturbation theory.
  • Findings highlight challenges in establishing quantum-classical correspondence for dynamic response phenomena.