广义库莫特模型中子系统的重置分析方法
Analytical approach to subsystem resetting in generalized Kuramoto models
AI总结：
本文提出分析库莫特型耦合振子系统中子系统重置的通用理论框架，探讨重置率、子系统大小及配置对稳态和相变的影响，揭示子系统重置可改变同步行为并产生非平凡特征。
摘要：
随机重置已成为驱动系统进入非平衡稳态并调节其性质的强大机制。尽管大多数现有研究关注全局重置，即同时重置所有自由度，但最近的研究表明，仅重置部分自由度（子系统重置）可定性地改变相互作用多体系统中的集体行为。本文开发了一个通用的理论框架，用于分析库莫特型耦合振子系统中的子系统重置。基于连续分数方法，我们推导出非重置子系统的稳态态参数自洽方程，适用于有噪声和无噪声动态以及任意相互作用谐波的模型。利用该框架，我们系统研究了稳态和相变如何依赖于重置率、子系统大小和重置配置。我们证明子系统重置可以移动或甚至抑制同步转变，并导致非平凡特征，如重新进入行为和相边界重构。在特定情况下，包括无噪声库莫特模型具有洛伦兹频率分布时，我们的结果恢复了已知的解析预测，并扩展到更一般的情况。这些结果确立了子系统重置作为在非平衡相互作用系统中工程集体动力学的多功能控制协议。
英文摘要：
Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are simultaneously reset, recent work has shown that resetting only a subset of degrees of freedom (subsystem resetting) can qualitatively alter collective behavior in interacting many-body systems. In this work, we develop a general theoretical framework for analysing subsystem resetting in Kuramoto-type coupled-oscillator systems. Building on a continued-fraction approach, we derive self-consistent equations for the stationary-state order parameter of the non-reset subsystem, applicable to both noisy and noiseless dynamics and to models with arbitrary interaction harmonics. Using this framework, we systematically investigate how the stationary state and phase transitions depend on the resetting rate, the size of the reset subsystem, and the reset configuration. We show that subsystem resetting can shift or even suppress synchronization transitions, and can give rise to nontrivial features such as re-entrant behavior and restructuring of phase boundaries. In specific cases, including the noiseless Kuramoto model with a Lorentzian frequency distribution, our results recover known analytical predictions and extend them to more general settings. These results establish subsystem resetting as a versatile control protocol for engineering collective dynamics in nonequilibrium interacting systems.
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