On a Boltzmann equation for Haldane statistics
Abstract
The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane 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 L1 solutions are obtained for the Cauchy problem. The main results concern existence, uniqueness and stability. Depending on the space dimension and the collision kernel, the results obtained are local or global in time.
Cite
@article{arxiv.1711.10357,
title = {On a Boltzmann equation for Haldane statistics},
author = {L. Arkeryd and A. Nouri},
journal= {arXiv preprint arXiv:1711.10357},
year = {2018}
}
Comments
24 pages. arXiv admin note: text overlap with arXiv:1406.0265 This is the published version of the paper. The condition (2.3) on the collision kernel is strengthened, as required for the result to hold