Archive ouverte HAL – Eigenfunction distribution for the Rosenzweig-Porter model

E. Bogomolny 1 M. Sieber 2

Physical Review E , American Physical Society (APS), 2018, 98 (3), 〈10.1103/PhysRevE.98.032139〉

The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. School of Mathematics [Bristol]