Non-linear Topological Geometry: A Quantum Dynamics Modeling Framework

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper explores the intersection of non-linear topological geometry and quantum dynamics, proposing a novel computational framework leveraging the inherent non-linear characteristics of topological structures to simulate complex physical systems. We introduce the concept of "quantum topology" – a state where topological properties are inherently quantized, and utilize this principle to model quantum systems' behavior within these structures. This work addresses limitations of traditional quantum simulation methods by offering a framework that explicitly incorporates non-linear dynamics and quantum effects, providing a new approach to understanding and modeling intricate physical phenomena. The core mechanism involves mapping topological invariants to quantum states and exploiting the non-linear nature of these states to generate realistic simulations. We demonstrate the framework's capability to generate complex topological structures and simulate quantum transitions within these structures, revealing subtle quantum effects not readily observable in conventional simulations.

DOI: 10.5281/zenodo.22264293

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