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arXiv · 2609.33396

An entropy-level method for quantitative time-asymptotic in the Fokker-Planck model for fermions -- appearance of non saturation

R. Alonso·B. Lods
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Abstract

In this contribution we consider the Fokker-Planck equation for fermions, commonly known as the Fermi-Dirac-Fokker-Planck equation. This equation is a correction of the classical Fokker-Planck model that incorporates the Pauli exclusion principle. We present a novel approach that combines three ingredients: (1) stability of solutions, (2) quantitative convergence for a dense set of initial data via a robust entropy method, and (3) a De Giorgi level-set iteration, to establish quantitative time-asymptotic thermalisation for general initial data. In particular, we prove quantitative convergence for arbitrarily cold initial data.

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R. Alonso, B. Lods. 2026-09-27. An entropy-level method for quantitative time-asymptotic in the Fokker-Planck model for fermions -- appearance of non saturation. https://arxiv.org/abs/2609.33396

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