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Computing the density of paths in complex systems.

Daniele Passerone1

  • 1Institute of Organic Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland. passero@oci.unizh.ch

The Journal of Chemical Physics
|April 15, 2006
PubMed
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This study introduces molecular dynamics algorithms to compute the density of paths, crucial for semiclassical quantum theory. These methods aid in understanding classical action and its fluctuations for realistic systems and rare events.

Area of Science:

  • Classical and Quantum Mechanics
  • Computational Physics

Background:

  • Classical trajectories are stationary points of the action integral (Hamilton's principle).
  • The second variation of the action quantifies fluctuations and path density.
  • Path density is vital in semiclassical quantum theory for weighting classical trajectory contributions.

Purpose of the Study:

  • To develop novel algorithms for computing the density of paths.
  • To apply these algorithms to realistic physical and chemical systems.
  • To explore applications in rare event phenomena.

Main Methods:

  • Utilizing molecular dynamics simulation concepts.
  • Developing two distinct algorithms for path density calculation.
  • Computing the van Vleck determinant.

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Main Results:

  • Successful computation of path density for realistic systems.
  • Demonstration of algorithms' efficacy in analyzing trajectory fluctuations.
  • Validation of the connection between classical action, fluctuations, and quantum propagation.

Conclusions:

  • The developed algorithms provide an efficient means to calculate path density.
  • This work bridges classical mechanics, semiclassical quantum theory, and computational methods.
  • Potential applications exist for studying rare events in physics and chemistry.