Invariant closure for the Fokker-Planck equation
Ilya V. Karlin, V.B. Zmievskii
TL;DR
This paper introduces a method based on dynamic invariance to derive closed-form moment equations from the Fokker-Planck equation, providing explicit formulas for eigenvalues and eigenfunctions for various potentials.
Contribution
It presents a novel application of the dynamic invariance principle to obtain closed moment equations and explicit eigenvalue formulas for the Fokker-Planck equation.
Findings
Derived explicit formulas for eigenvalues and eigenfunctions for arbitrary potentials.
Established a systematic approach to close moment equations from the Fokker-Planck equation.
Demonstrated the effectiveness of the method in theoretical analysis.
Abstract
We develop the principle of dynamic invariance to obtain closed moment equations from the Fokker-Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Statistical Mechanics and Entropy · Quantum chaos and dynamical systems