We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model, we analyze tagged-particle diffusion in a single file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the “confining” (all background particles in front of the tagged-particle) and “pushing” (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.

中文翻译：

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双稳态势中的单文件扩散：标记粒子的屏障穿越中的记忆特征

我们研究了在过阻尼环境中穿越障碍的记忆效应。我们关注的场景中，隐藏的自由度在与可观察的时间完全相同的时间尺度上放松。作为一个原型模型，我们在一个双稳态势能范围内的单个文件中分析标记粒子的扩散。我们确定记忆的特征并解释其起源。出现的记忆是集体多体本征模投影到标记粒子运动上的结果。我们对“限制”（所有背景粒子在标记粒子前面）和“推动”（所有背景粒子在标记粒子后面）场景感兴趣，在这些场景中，我们发现了非平凡且质上不同的松弛行为。值得注意的是，在固定的粒子数下，我们发现势垒越高，记忆效果越强。外部电势会改变内存这一事实更普遍，这一点很重要，在广义Langevin方程的应用中应予以考虑。我们的结果可以很容易地通过实验进行测试，并且可能对理解生物离子通道中的转运具有重要意义。