发表机构
Sapienza Università di Roma; Istituto Nazionale di Fisica Nucleare, Sezione Roma 1（罗马第一大学; 意大利国家核物理研究所，罗马一分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过将非马尔可夫最优路径映射为哈密顿系统，为活性物质中的稀有事件提供了精确的动力学描述，并揭示了非零能量下的闭合周期轨道这一独特特征。
AI 中文摘要
活性系统通过非平衡涨落穿越复杂环境，使得标准的平衡态跃迁速率理论不再适用。此外，跃迁速率仅提供关于非平衡动力学如何探索亚稳态的部分信息，而最优路径的知识则能提供更深刻的物理洞察。以活性Ornstein-Uhlenbeck粒子作为范式模型，即由指数相关噪声驱动的随机动力学，我们将非马尔可夫最优路径精确映射到高维哈密顿动力学系统，从而对于任意力场，可以通过求解相应的哈密顿方程系统地计算最优路径。调节守恒能量使我们能够探索多种动力学机制：从严格限制在零能量面上的经典瞬子轨迹，到仅在非零能量下出现的闭合周期轨道，这代表了非马尔可夫活性动力学的独特特征。
英文摘要
Active systems navigate complex environments through non-equilibrium fluctuations, rendering standard equilibrium transition-rate theories inadequate. Moreover, transition rates provide only partial information on how stochastic dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper physical insight. Using an active Ornstein-Uhlenbeck particle, i.e., a particle driven by exponentially correlated noise, as a paradigmatic model, we establish an exact mapping of the non-Markovian optimal path onto a higher-dimensional Hamiltonian dynamical system so that, for arbitrary force fields, optimal paths can be computed systematically by solving the corresponding Hamilton equations. Tuning the conserved energy allows us to explore diverse dynamical regimes, ranging from classical instanton trajectories strictly confined to the zero-energy surface to finite-time optimal paths at non-zero energies, which can spiral around shoulders of the energy landscape, a distinct signature of the non-Markovian active dynamics.
