# Multifractality of open quantum systems

## TL;DR

This paper investigates the multifractal properties of eigenstates in open quantum systems with pseudointegrable classical dynamics, revealing a hierarchical structure and guiding experimental observation of multifractality.

## Contribution

It extends the framework for open chaotic quantum maps to pseudointegrable systems, establishing a relationship between eigenstates and classical structures with multifractal characteristics.

## Key findings

- Eigenstates are related to classical structures hierarchically.
- Resonance states exhibit multifractality at small scales.
- Guidance for experimental detection of multifractal behavior.

## Abstract

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.