Brownian systems perturbed by mild shear: Comparing response relations

Non-equilibrium statistical mechanics of the heat bath for two Brownian particles

We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a `system' is both perturbed and sensed by the Brownian particles. Non-local thermal fluctuation give rise to bath-mediated static forces between the particles. Based on the general sum-rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles' dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment …

二维活性布朗粒子穿越抛物线障碍：有限矩形域中具有吸收边界条件

Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions

研究二维活性布朗粒子在有限矩形域中穿越抛物线障碍的动力学行为，通过扰动理论求解福克-普肯杰方程，分析活动性对生存概率和首次通过时间分布的影响。

Rapid-Prototyping a Brownian Particle in an Active Bath

Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length scales of usual active matter systems. A particle diffusing in a harmonic potential generated by an optical trap is kicked by programmed forces with time correlation at random intervals following the Poisson process. The model's generic simplicity allows us to find conditions for which displacements are Gaussian (or not), how diffusion is perturbed (or not) b…

二维活性布朗粒子跨越抛物线障碍：过渡路径时间、生存概率和首次通过时间

Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Transition-Path Times, Survival Probability, and First-Passage Time

本文研究了二维活性布朗粒子跨越抛物线障碍的过渡路径时间、生存概率和首次通过时间，揭示了活动性对这些特性的影响。

The eigenvectors of Gaussian matrices with an external source

We consider a diffusive matrix process $(X_t)_{t\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t)_{t\ge 0}$ is a Hermitian Brownian motion. The matrix $A$ is the "external source" that one would like to estimate from the noisy observation $X_t$ at some time $t>0$. We investigate the relationship between the non-perturbed eigenvectors of the matrix $A$ and the perturbed eigenstates at some time $t$ for the three relevant scaling relations between the time $t$ and the dimension $N$ of the matrix $X_t$. We determine the asymptotic (mean-squared) projec…

吸收边界圆形区域内的活性布朗粒子

Active Brownian Particles in a Circular Disk with an Absorbing Boundary

该研究通过微扰方法求解活性布朗粒子在吸收边界圆形区域内的Fokker-Planck方程，获得传播子、存活概率和首次通过时间分布，揭示了活性与旋转扩散率对非平衡动力学的影响。