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Variational supersymmetric approach to evaluate Fokker–Planck probability

Author

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  • Borges, G.R.P.
  • Filho, Elso Drigo
  • Ricotta, R.M.

Abstract

In this work we introduce a method to determine the time dependent probability density for the one-dimensional Fokker–Planck equation. The treatment is based in an analysis of the Schrödinger equation through the variational method associated to the formalism of supersymmetric quantum mechanics (SQM). The approach uses an ansatz for the superpotential which allows us to obtain the trial functions of the variational method. The hierarchy of effective Hamiltonians permits us to determine the variational eigenfunctions and energies of the excited states to the evaluation of the probability. The symmetric bistable potential is used to illustrate the approach whose results are compared with results obtained by the state-dependent diagonalization method and by direct numerical calculation.

Suggested Citation

  • Borges, G.R.P. & Filho, Elso Drigo & Ricotta, R.M., 2010. "Variational supersymmetric approach to evaluate Fokker–Planck probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3892-3899.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:18:p:3892-3899
    DOI: 10.1016/j.physa.2010.05.027
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    Cited by:

    1. Philipp, Lucas & Shizgal, Bernie D., 2019. "A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 158-166.
    2. Heidari, Hossein & Karamati, Mahdi Rezaei & Motavalli, Hossein, 2022. "Tumor growth modeling via Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    3. Polotto, Franciele & Drigo Filho, Elso & Chahine, Jorge & Oliveira, Ronaldo Junio de, 2018. "Supersymmetric quantum mechanics method for the Fokker–Planck equation with applications to protein folding dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 286-300.

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