发表机构
Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对重置布朗搜索者，发现目标通过调整运动的相关时间（而非探索范围）可最大化平均捕获时间，从而延长生存，揭示了时间相关性作为逃避资源的作用。
AI 中文摘要
返回熟悉的位置可以帮助搜索者找到目标——但目标应如何移动以避免被发现？我们针对一个重置的布朗搜索者和一个围绕其家位置波动的移动目标来回答这个问题。在保持目标典型探索范围固定的情况下，我们发现平均捕获时间在中间相关时间处达到最大：快速运动促进遭遇，而慢速运动使目标实际上保持静止。在这两个极端之间，远离搜索者重置点的持续偏离可以显著延迟捕获。解析极限结果解释了这一最优现象，而数值解揭示了最大平均捕获时间与最优相关时间在多个数量级上近似线性关系。这些发现将时间相关性视为逃避的资源，允许目标通过改变其移动方式而非漫游范围来延长生存。
英文摘要
Returning to a familiar location can help a searcher find its target---but how should the target move to avoid being found? We address this question for a resetting Brownian searcher and a mobile target fluctuating around a home location. Keeping the target's typical exploration range fixed, we find that the mean capture time is maximized at an intermediate correlation time: rapid motion promotes encounters, whereas slow motion leaves the target effectively stationary. Between these extremes, persistent excursions away from the searcher's reset point can substantially delay capture. Analytical limiting results explain this optimum, while numerical solutions reveal an approximately linear relation between the maximal mean capture time and the optimal correlation time across many decades. These findings identify temporal correlations as a resource for evasion, allowing a target to prolong survival by changing how it moves rather than where it roams.
Comments6 pages, 4 figures
