# An exactly solvable quantum-metamaterial type model

## TL;DR

This paper presents an exactly solvable model of a fractal quantum metamaterial interacting with electromagnetic fields, using Haar and Wigner-Weyl transforms to address complex quantum correlations.

## Contribution

It introduces a novel exactly solvable model of a quantum metamaterial with fractal structure, advancing understanding of quantum coherence in complex systems.

## Key findings

- Exact solution achieved using Haar and Wigner-Weyl transforms.
- Finite-size precursors to fractal quantum structures studied.
- Insights into quantum correlations in large coherent systems.

## Abstract

The key difficulty in the modelling of large quantum coherent structures lies in keeping track of nonlocal, multipoint quantum correlations between their constituent parts. Here we consider a special case of such a system, a fractal quantum metamaterial interacting with electromagnetic field, and show that it can be exactly solved by using a combination of the Haar transform and the Wigner-Weyl transform. Theoretical and experimental investigation of finite-size precursors to exactly solvable fractal quantum structures as this will help illuminate the behaviour of generic quantum coherent structures on a similar spatio-temporal scale.