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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19976310 |
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Table of Contents:
- <p>本文以「时间最优约束」为运动底层公理,突破经典力学受力分析的单一视角,重新诠释最速曲线、单摆、双摆及多体系统的秩序与混沌本质,明确时间对运动的核心约束内涵:时间不干预轨迹几何形态,仅限定物体在既定力学与空间约束下,以耗时最短的方式完成空间位置演化,该规律为物质运动的天然固有法则,而非物体主观选择的行为策略。基于该公理体系,系统阐明单体有序运动与多体混沌涌现的内在机理,构建以单体最优耗时泛函、最优偏离量、系统混乱系数为核心的完整量化模型,实现多体混沌强度的统一数理表征;依托变分原理建立有序–混沌临界稳定性判据,精准界定多体系统稳定运行的参数边界。研究表明,多体混沌并非基础运动法则失效,而是多个独立运动主体各自恪守时间最优约束,局部最优路径相互干涉、冲突叠加所形成的必然涌现结果。本文为多体力学混沌问题提供了从底层第一性原理到定量判定的全新研究范式,理论自洽性强,兼具基础理论创新与跨领域工程应用价值。<br><br></p> <p>时间晶体(包括离散时间晶体 DTC)的核心特征是时间平移对称性的自发破缺——系统在周期驱动下,演化周期为驱动周期的整数倍,且时间关联函数不衰减。<br>本文“扇骨共用–焦点分裂”框架,将这一代数描述等价地翻译为构型空间的几何拓扑语言,建立了从有序相、热化相到相变点的完整映射。</p> <p>The core feature of time crystals (including Discrete Time Crystals, DTC) lies in the spontaneous breaking of time-translation symmetry. Under periodic driving, the evolution period of the system is an integer multiple of the driving period, and the time correlation function exhibits non-decaying behavior.</p> <p>In this paper, we propose the framework of Rib Shared Structure – Focus Splitting, which equivalently translates this algebraic description into the geometric topological language on configuration space, establishing a complete mapping covering the ordered phase, thermalized phase and phase transition point.</p>