Analysis of reflection coefficients for the Fokker-Planck equation

Abstract

Mathematical structure of the reflection coefficients for the one-dimensional Fokker-Planck equation is studied. A new formalism using differential operators is introduced and applied to the analysis in high- and low-energy regions. Formulas for high-energy and low-energy expansions are derived, and expressions for the coefficients of the expansion, as well as the remainder terms, are obtained for general forms of the potential. Conditions for the validity of these expansions are discussed on the basis of the analysis of the remainder terms.

Cited by in corpus (5)

• Low-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schrödinger equations
• High-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schrödinger equations
• Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with periodic potentials
• Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation
• Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with asymptotically periodic potentials