Analysis of reflection coefficients for the Fokker-Planck equation

Details Analysis of reflection coefficients for the Fokker-Planck equation Analysis of reflection coefficients for the Fokker-Planck equation

2011-12-26

arxiv.org/abs/1112.5834v1

J. Phys. A: Math. Gen. 39 (2006) 7015-7037; Corrigendum: J. Phys. A: Math. Gen. 39 (2006) 15059

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/39/22/015 10.1

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.

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