# Quantum multiresolution: tower of scales

## TL;DR

This paper explores the formation and control of complex quantum patterns and states using a hierarchical approach, combining numerical simulations and algebraic methods to understand their stability and behavior.

## Contribution

It introduces a novel quantum multiresolution framework that generates and manipulates diverse stable states from fundamental localized modes.

## Key findings

- Demonstrated creation of stable and chaotic quantum states
- Controlled pattern behavior via algebraic reduction
- Numerical evidence of symmetry-driven pattern formation

## Abstract

We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like equations. The numerical simulation demonstrates the formation of various (meta) stable patterns or orbits generated by internal hidden symmetry from generic high-localized fundamental modes. In addition, we can control the type of behavior on the pure algebraic level by means of properly reduced algebraic systems (generalized dispersion relations).