Pattern Formation in Quantum Ensembles

TL;DR

This paper introduces analytical and numerical methods to describe complex behavior and pattern formation in classical and quantum ensembles, including stable states, chaos, and entanglement, using a hierarchy of quantum equations.

Contribution

It develops a novel framework combining analytical and numerical techniques for modeling pattern formation in quantum and classical systems based on the quantum hierarchy.

Findings

Demonstration of nontrivial stable and chaotic states

Explicit analytical and numerical descriptions of quantum dynamics

Application to various collective models from quantum hierarchy

Abstract

We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of ``wignerization'' procedure of classical BBGKY hierarchy. We present the explicit description of internal quantum dynamics by means of exact analytical/numerical computations.