The Generalized Fokker-Planck Equation in terms of Dunkl-type Derivatives
R. D. Mota, D. Ojeda-Guill\'en, M. A. Xicot\'encatl
TL;DR
This paper introduces two generalized Fokker-Planck equations using Dunkl-type derivatives with reflection operators, providing exact solutions for harmonic oscillator and centrifugal potentials, expanding the mathematical framework of stochastic processes.
Contribution
The work develops two new generalizations of the Fokker-Planck equation employing Dunkl-type derivatives, offering exact solutions for specific potentials.
Findings
Exact solutions for harmonic oscillator potential
Exact solutions for centrifugal-type potential
Extension of Fokker-Planck framework using Dunkl derivatives
Abstract
In this work we introduce two different generalizations of the Fokker-Planck equation in (1+1) dimensions by replacing the spatial derivatives in terms of generalized Dunkl-type derivatives involving reflection operators. As applications of these results, we solve exactly the generalized Fokker-Planck equations for the harmonic oscillator and the centrifugal-type potentials.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Statistical Mechanics and Entropy · Quantum chaos and dynamical systems