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Variational principle for stochastic wave and density equations.

Joshua Wilkie1

  • 1Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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We introduce a stochastic McLachlan variational principle to derive wave equations and achieve probability-preserving decompositions for vibrational dynamics. This method accurately models systems with pairwise interactions.

Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Computational Chemistry

Background:

  • Variational principles are fundamental in physics for deriving equations of motion.
  • Stochastic processes are crucial for modeling systems with inherent randomness.
  • The McLachlan variational principle is a powerful tool in classical and quantum mechanics.

Purpose of the Study:

  • To develop a stochastic generalization of the McLachlan variational principle.
  • To demonstrate its utility in deriving known stochastic wave equations.
  • To obtain an exact probability-preserving stochastic density decomposition for vibrational dynamics.

Main Methods:

  • Stochastic generalization of the McLachlan variational principle.
  • Derivation of stochastic wave equations.

Related Experiment Videos

  • Development of a probability-preserving stochastic density decomposition.

    • Main Results:

    • The stochastic McLachlan variational principle successfully derives known stochastic wave equations.
    • An exact probability-preserving stochastic density decomposition is obtained for vibrational dynamics.
    • The method is applicable to problems with pairwise interactions.

    Conclusions:

    • The developed stochastic variational principle offers a novel approach to stochastic dynamics.
    • This framework provides a rigorous method for analyzing vibrational dynamics with stochasticity.
    • The probability-preserving decomposition is a significant advancement for computational modeling.