We study the non-equilibrium steady states and first passage properties of a Brownian particle with position $X$ subject to an external confining potential of the form $V(X)=\mu|X|$, and that is switched on and off stochastically. Applying the potential intermittently generates a physically realistic diffusion process with stochastic resetting toward the origin, a topic which has recently attracted a considerable interest in a variety of theoretical contexts but has remained challenging to implement in lab experiments. The present system exhibits rich features, not observed in previous resetting models. The mean time needed by a particle starting from the potential minimum to reach an absorbing target located at a certain distance can be minimized with respect to the switch-on and switch-off rates. The optimal rates undergo continuous or discontinuous transitions as the potential stiffness $\mu$ is varied across non-trivial values. A discontinuous transition with metastable behavior is also observed for the optimal stiffness at fixed rates.

中文翻译：

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间歇性复位电位

我们研究了位置为 $X$ 的布朗粒子的非平衡稳态和首次通过特性，该粒子受到 $V(X)=\mu|X|$ 形式的外部约束势的影响，并且该粒子被打开和关闭随机地。间歇性地应用势能产生物理真实的扩散过程，随机重置到原点，这个话题最近在各种理论背景下引起了相当大的兴趣，但在实验室实验中实施仍然具有挑战性。本系统表现出丰富的功能，在以前的重置模型中没有观察到。粒子从潜在最小值开始到达位于特定距离处的吸收目标所需的平均时间可以相对于开启和关闭速率最小化。最佳速率经历连续或不连续的转变，因为潜在刚度 $\mu$ 在非平凡值之间变化。对于固定速率下的最佳刚度，还观察到具有亚稳态行为的不连续转变。