On a Boltzmann equation for Haldane statistics

Leif Arkeryd; Anne Nouri

doi:10.3934/krm.2019014

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2019, Volume 12, Issue 2: 323-346. Doi: 10.3934/krm.2019014

This issue Previous Article Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion Next Article Non-uniqueness of weak solutions of the Quantum-Hydrodynamic system

On a Boltzmann equation for Haldane statistics

Leif Arkeryd^1, and
Anne Nouri^2,

1.
Mathematical Sciences, 41296 Göteborg, Sweden
2.
Aix-Marseille University, CNRS, Centrale Marseille, I2M UMR 7373, 13453 Marseille, France

Received: December 31, 2017

Revised: May 31, 2018

Published: March 2019

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Abstract

The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper Haldane [10] proposed a definition based on a generalization of the Pauli exclusion principle for fractional quantum statistics. The present paper is a study of quantum quasi-particles obeying Haldane statistics in a fully non-linear kinetic Boltzmann equation model with large initial data on a torus. Strong $L^1$ solutions are obtained for the Cauchy problem. The main results concern existence, uniqueness and stabililty. Depending on the space dimension and the collision kernel, the results obtained are local or global in time.

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Mathematics Subject Classification: 82C10, 82C22, 82C40.

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References

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