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Variational perturbation theory for Markov processes.

Hagen Kleinert1, Axel Pelster, Mihai V Putz

  • 1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany. kleinert@physik.fu-berlin.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 22, 2002
PubMed
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We introduce a new convergent variational perturbation theory for Markov processes. This method accurately models particle diffusion in complex, anharmonic potentials.

Area of Science:

  • Physics
  • Physical Chemistry
  • Applied Mathematics

Background:

  • Markov processes are fundamental in modeling systems with memoryless transitions.
  • Understanding conditional probability densities is crucial for predicting system evolution.
  • Perturbation theory offers a powerful, yet often limited, approach for complex systems.

Purpose of the Study:

  • To develop a novel convergent variational perturbation theory.
  • To provide a robust framework for calculating conditional probability densities in Markov processes.
  • To demonstrate the theory's efficacy on a challenging physical system.

Main Methods:

  • Development of a convergent variational perturbation theory.
  • Application to the specific case of a particle diffusing in an anharmonic potential.

Related Experiment Videos

  • Utilizing principles of variational methods and perturbation expansions.

    • Main Results:

    • The developed theory provides accurate conditional probability densities.
    • The theory successfully handles the complexities of anharmonic potentials.
    • Demonstrated convergence and accuracy of the variational perturbation approach.

    Conclusions:

    • The convergent variational perturbation theory is a powerful new tool for analyzing Markov processes.
    • This approach offers significant advantages for systems with complex potentials.
    • The findings have implications for statistical mechanics and computational physics.