Eigenfunction distribution for the Rosenzweig-Porter model

TL;DR

This paper derives explicit formulas for the distribution of eigenfunctions in the Rosenzweig-Porter model, revealing fractal behavior and matching numerical results, thus providing rare closed-form solutions in this context.

Contribution

It presents the first closed-form eigenfunction distribution for the Rosenzweig-Porter model in the fractal regime, based on simple physical principles.

Findings

Explicit eigenfunction distribution formulas derived

Results agree well with numerical simulations

Provides rare closed-form solutions for complex eigenfunction behavior

Abstract

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.