Abstract

A fully nonlinear kinetic Boltzmann equation for anyons is studied in a periodic one-dimensional setting with large initial data. Strong $L^1$ solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and stability. We use the Bony functional, the two-dimensional velocity frame specific for anyons, and an initial layer analysis that moves the solution away from a critical value.

Keywords

  1. anyon
  2. Haldane statistics
  3. low temperature kinetic theory
  4. quantum Boltzmann equation

MSC codes

  1. 82C10
  2. 82C22
  3. 82C40

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Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 4720 - 4742
ISSN (online): 1095-7154

History

Submitted: 13 March 2015
Accepted: 30 September 2015
Published online: 15 December 2015

Keywords

  1. anyon
  2. Haldane statistics
  3. low temperature kinetic theory
  4. quantum Boltzmann equation

MSC codes

  1. 82C10
  2. 82C22
  3. 82C40

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