Self-similarity under inflation and level statistics: a study in two dimensions

TL;DR

This paper investigates the energy level spacing statistics of a two-dimensional quasiperiodic tiling, utilizing self-similarity under inflation to derive recursion relations and define new distribution functions through combined numerical and analytical methods.

Contribution

It introduces a novel approach to analyze level statistics in quasiperiodic structures using self-similarity and develops new distribution functions with both numerical and analytical insights.

Findings

Derived recursion relations for level spacing distributions

Defined new distribution functions for quasiperiodic tilings

Combined numerical and analytical methods to analyze level statistics

Abstract

Energy level spacing statistics are discussed for a two dimensional quasiperiodic tiling. The property of self-similarity under inflation is used to write a recursion relation for the level spacing distributions defined on square approximants to the perfect quasiperiodic structure. New distribution functions are defined and determined by a combination of numerical and analytical calculations.