Soutenance de thèse: Shuang Wu


14:30 - 17:00

IPN-batiment 100, Auditoriurm
15 Rue Georges Clemenceau, orsay

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Soutenance de thèse:

Algebraic area distribution of two dimensional random walks and the Hofstadter model


Shuang Wu


  • Rapporteur: Sergei Matveenko (Landau Institute for Theoretical Physics, Moscow, Russia)
  • Rapporteur: Alexios Polychronakos  (The City College of New York, USA)
  • Examinateur: Angel Alastuey (Laboratoire de Physique, ENS Lyon)
  • Examinateur: Vincent Pasquier (IPhT, CEA Saclay)
  • Examinatrice: Didina Serban (IPhT, CEA Saclay)
  • Invité: Olivier Giraud (LPTMS, Université Paris-Sud)
  • Directeur de thèse: Stéphane Ouvry (LPTMS, Université Paris-Sud)

This thesis is about the Hofstadter model, i.e, a single electron moving on a two-dimensional lattice coupled to a perpendicular homogeneous magnetic field. Its spectrum is one of the famous fractals in quantum mechanics, known as the Hofstadter’s butterfly. There are two main subjects in this thesis: the first is the study of the deep connection between the Hofstadter model and the distribution of the algebraic area enclosed by two-dimensional random walks. The second focuses on the distinctive features of the Hofstadter’s butterfly and the study of the bandwidth of the spectrum. We found an exact expression for the trace of the Hofstadter Hamiltonian in terms of the Kreft coefficients, and for the higher moments of the bandwidth.

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