Quantum-Enhanced Geometric Analysis of Non-Linear Dynamics

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper explores the application of quantum mechanics to enhance geometric analysis of non-linear dynamical systems. We propose a novel method, the 'quantum-induced curvature' operator, that leverages quantum effects to uncover hidden geometric structures within these systems. The core claim is that incorporating quantum principles can provide a deeper understanding of the evolution of non-linear dynamics compared to traditional analytical methods. This investigation utilizes a mathematical framework based on the principles of quantum field theory and differential geometry to demonstrate the potential for significant insights in this field. The paper details the design of the operator, its mathematical formulation, and preliminary results illustrating its impact on analyzing complex systems exhibiting non-linear behavior. The analysis emphasizes the potential for identifying emergent geometric patterns that are difficult to discern with conventional techniques.

DOI: 10.5281/zenodo.22185220

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