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Quantum拓扑的自适应几何建模 (Adaptive Quantum Topology Geometric Modeling)

Jincheng Zhang

Published Sep 4, 2026• 0 citations
Publisher

Abstract

Quantum拓扑,一种量子力学中的概念,具有奇特的几何结构,被认为是量子世界中一种独特的特性。这种结构的存在使得量子拓扑的几何建模成为一个极具挑战性和潜在价值的研究领域。本文提出了一种基于量子拓扑的自适应几何建模技术,旨在通过动态调整几何表示和建模来模拟和理解量子拓扑的复杂特性。该技术利用量子拓扑的性质,实现几何表示的动态调整,从而能够有效地建模和计算量子拓扑的各种现象。该研究旨在探索利用量子拓扑的优势,构建更强大的量子拓扑建模工具,并推动量子拓扑的理论和应用研究。

DOI
10.5281/zenodo.22294388

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Quantum拓扑,一种量子力学中的概念,具有奇特的几何结构,被认为是量子世界中一种独特的特性。这种结构的存在使得量子拓扑的几何建模成为一个极具挑战性和潜在价值的研究领域。本文提出了一种基于量子拓扑的自适应几何建模技术,旨在通过动态调整几何表示和建模来模拟和理解量子拓扑的复杂特性。该技术利用量子拓扑的性质,实现几何表示的动态调整,从而能够有效地建模和计算量子拓扑的各种现象。该研究旨在探索利用量子拓扑的优势,构建更强大的量子拓扑建模工具,并推动量子拓扑的理论和应用研究。
This paper explores the application of quantum topology to the modeling of geometric morphology, presenting a novel technique for dynamically adjusting geometric features based on data. Traditional modeling approaches are static, requiring manual feature engineering and often lacking the ability to adapt to complex datasets. Quantum topology offers a fundamentally different approach – a system of interconnected, conserved states – that allows for continuous, self-adaptive geometric representation. We detail the theoretical framework, algorithm implementation, and preliminary results demonstrating the efficacy of this method in analyzing and manipulating geometric patterns within complex datasets. The core claim centers around the creation of a quantum topology-based self-adaptive geometric modeling technique that dynamically adjusts geometric morphology based on data. This approach promises to enhance data analysis and representation through continuous, intelligent geometric adjustment.
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摘 要:本文系统构建量子经济学的数学基础与理论框架,衔接量子力学与经济金融实践。首先阐述希尔伯特空间、线性算子、复变函数、密度矩阵等核心数学工具的经济内涵,奠定理论基石;进而建立单主体叠加态与多主体张量积态、纠缠态的经济系统表示方法,揭示观测导致的量子坍缩对经济状态的影响;基于薛定谔方程与时间演化算子,刻画经济系统的动态演化规律,结合退相干理论解释确定性演化机制;通过叠加、测不准、纠缠等量子原理解析经济系统的非线性关联与瞬时联动等经典难题;最后构建量子资产定价和量子博弈论等高级模型并实证验证。研究突破经典经济学线性化、确定性范式局限,为经济复杂行为分析提供全新视角与可操作工具,适用于经济学、金融学等领域的理论研究与实践应用。 关键词:量子经济学;希尔伯特空间;概率幅;密度矩阵;薛定谔方程
Quantum topology, a fascinating field of physics, explores the interplay between quantum mechanics and topology. Recent research has highlighted the potential of manipulating spacetime through quantum phenomena, leading to novel geometric properties. This paper investigates the application of adaptive geometric simplification, leveraging the unique properties of quantum entanglement, to restructure and simplify topological structures. Specifically, we propose a method that utilizes quantum entanglement to subtly alter the underlying geometry, providing a new computational framework for analyzing and manipulating topological systems. This approach aims to offer a fundamentally different approach to understanding and modeling topological phenomena, potentially revealing insights into their robustness and adaptability. The core claim is that the combined effect of quantum entanglement and adaptive geometric simplification leads to simplified, more robust topological structures, and provides a novel computational model.
摘 要:主流经济学因果认知先后经历决定论因果与概率因果两次革命,二者共享经典力学世界观的强本体论预设:因果关系客观先在、变量可独立分离、观测行为中立无扰、因果作用局域链式传递。这使得现代实证因果推断始终面临内生性无解、预期自实现、观测干预扭曲与非局部联动失效等底层困境。本文突破传统框架,原创性提出经济学意义上的量子因果论,将经济因果关系重构为因果叠加、因果纠缠与观测坍缩共同规定的量子态演化过程。文章严格证明:经典确定性因果是量子因果在“高频观测、大规模平均、强制度约束”条件下的统计近似;概率因果则是量子因果在“弱叠加、弱纠缠、弱观测干扰”情形下的退化特例。本文构建量子因果的公理体系、态空间表示、因果相干性判据与观测坍缩机制,首次提出经济退相干原理,有效化解量子叠加性与日常确定性因果的表观矛盾。研究表明,量子因果论能够统一解释从个体决策到宏观波动、从市场均衡到系统性风险的所有经济现象,为重新理解内生性、预期效应、政策传导与系统风险提供一般化基础,也为中国自主经济学知识体系构建提供具有范式革新意义的理论工具。 关键词:量子因果论;因果叠加;因果纠缠;观测坍缩;经济退相干