Exact relations between multifractal exponents at the Anderson transition

TL;DR

This paper establishes two exact relations between multifractal exponents at the Anderson transition, revealing a symmetry in the spectrum and linking wave function multifractality to Wigner delay times.

Contribution

It presents novel exact relations between multifractal exponents at the critical point of the Anderson transition, enhancing understanding of wave function properties.

Findings

Symmetry linking multifractal exponents for q<1/2 and q>1/2

Connection between wave function multifractality and Wigner delay times

Exact relations hold at the critical point of the Anderson transition

Abstract

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with indices $q<1/2$ to those with $q>1/2$. The second relation connects the wave function multifractality to that of Wigner delay times in a system with a lead attached.