# Geometry of Quantum Riemannian Hamiltonian Evolution

## TL;DR

This paper explores the geometric structure of quantum Hamiltonian evolution, extending classical stability methods to quantum systems, and demonstrates through simulations that this approach aligns well with classical results, contributing to quantum chaos understanding.

## Contribution

It introduces a quantum geometric framework for Hamiltonian evolution and validates it through simulations, bridging classical and quantum stability analyses.

## Key findings

- Quantum geometric methods align with classical stability results
- Simulations confirm the approach's effectiveness for quantum systems
- Provides new insights into quantum chaos phenomena

## Abstract

This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these show that the quantum mechanical extension of the classical method, for which trajectories are plotted as expectation values of the corresponding quantum operators, appears to work well, providing results consistent with the corresponding classical problems. The results appear to provide a new contribution to the subject of quantum chaos.