布朗陀螺仪中电流涨落的最优探测尺度
Optimal probing scale for current fluctuations in a Brownian gyrator
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中文总结 AI 辅助
本文研究布朗陀螺仪中电流涨落的最优探测尺度，通过四极剪切探针将响应与代价分离，得到闭式最优半径，并由系统较快时钟决定，经模拟验证。
中文摘要 AI 辅助
一个受驱动的胶体转子维持着循环电流，人们希望对其涨落加以约束。任何此类约束都取决于电流对扰动的响应强度以及该扰动所付出的额外耗散代价，因此存在一个明确的问题：应在何处施加扰动？单位Onsager-Machlup代价的响应取决于探针作用的半径，并在某个确定的半径处达到最大值。我们针对布朗陀螺仪以及高斯包络下的四极剪切流回答了这一问题，该探针的设计使得线性响应在每个观测窗口内对其完全不可见，因此整个信号为二阶效应。该问题可分离：代价是径向的，不依赖于循环；而响应位于$m=3$角向扇区，其中预解式化简为$b=4$的Kummer方程，磁化率是包络宽度的超几何函数。最大化比值给出了闭式的最优探测半径。它由系统中两个时钟中较快者决定：对于弱驱动，$r^*=1.1264\sqrt{D/\gamma}$，即陷阱的热半径；对于强驱动，$r^*=1.5563\sqrt{D/\Omega}$，即旋转一弧度所扩散的距离，而陷阱刚度完全消失。交叉发生在$\Omega=\gamma$处。两个极限及其前置因子均通过直接模拟得到验证。
英文摘要
A driven colloidal rotor sustains a circulating current whose fluctuations one would like to bound. Any such bound rests on how strongly the current responds to a perturbation and on how much extra dissipation that perturbation costs, so there is a well-posed question of where to push: the response per unit Onsager-Machlup cost depends on the radius at which the probe acts, and is maximised at a definite one. We answer this for the Brownian gyrator and a quadrupolar shear under a Gaussian envelope, a probe chosen so that linear response is exactly blind to it at every observation window, so that the entire signal is second order. The problem separates: the cost is radial and does not see the circulation, while the response lives in the $m=3$ angular sector, where the resolvent reduces to Kummer's equation with $b=4$ and the susceptibility is a hypergeometric function of the envelope width. Maximising the ratio gives the optimal probing radius in closed form. It is set by whichever of the system's two clocks is faster: for weak driving $r^*=1.1264\sqrt{D/γ}$, the thermal radius of the trap, and for strong driving $r^*=1.5563\sqrt{D/Ω}$, the distance diffused in one radian of rotation, with the trap stiffness dropping out entirely. The crossover is at $Ω=γ$. Both limits, and the prefactors, are confirmed against direct simulation.
