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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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Cite

BibTeXRIS
BibTeX
@misc{alonso2026entropylevel,
  title = {{An entropy-level method for quantitative time-asymptotic in the Fokker-Planck model for fermions -- appearance of non saturation}},
  author = {R. Alonso and B. Lods},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33396},
  eprint = {2609.33396},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33396},
}
RIS
TY  - UNPB
TI  - An entropy-level method for quantitative time-asymptotic in the Fokker-Planck model for fermions -- appearance of non saturation
AU  - R. Alonso
AU  - B. Lods
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33396
UR  - https://arxiv.org/abs/2609.33396
AB  - 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.
ER  -