Quantum dynamics of the harmonic oscillator on a cylinder

TL;DR

This paper investigates the complex quantum dynamics of a particle in a harmonic oscillator potential confined to a cylindrical surface, revealing intricate and chaotic-like behavior of quantum averages over time.

Contribution

It provides a detailed analysis of the evolution of coherent states on a cylindrical geometry, highlighting the complex and chaotic-like trajectories of quantum averages.

Findings

Quantum averages exhibit complex, chaotic-like trajectories.

Discontinuous phase changes lead to intricate evolution patterns.

The behavior resembles chaos in quantum dynamics.

Abstract

Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a parallel (circle) the trajectory pattern of quantum averages specifying coordinates on a cylinder is very complex and in some aspects resembles chaotic one.