Observation of super-ballistic Brownian dynamics in liquid

Brownian motion is a foundational physical process characterized by a mean-squared displacement that scales linearly in time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic, scaling as t2. This effect was predicted by Einstein in 1907 and recently observed experimentally. We report that this picture is only true on average; by conditioning specific initial velocities, we predict theoretically and confirm by experiment that the mean squared displacement becomes super-ballistic, with a power scaling law of t5/2. This result is due to the colored noise of incompressible fluids, resulting in a non-zero first moment for the thermal force when conditioned on non-zero initial velocities. These results are a first step towards unraveling the non-equilibrium dynamics of fluids.
, , , # Observation of super-ballistic Brownian dynamics in liquid

Dataset DOI: [10.5061/dryad.pvmcvdnz4](10.5061/dryad.pvmcvdnz4)

## Description of the data and file structure

We have constructed an optical trap for microspheres in a microfluidic chamber. We tracked the position of the trapped sphere below its momentum relaxation time and digitized the analog signal. We then conditioned on initial velocities to study short-time Brownian motion. 

### Files and variables

#### File: noise_velocity.csv

**Description:**  Experimental velocity time traces but with no particle trapped. Demonstrates the system's noise due to the laser shot noise and other low frequency noise sources.

##### Variables

* Trace 1: Independent velocity time trace with 750 ns time step.
* Trace 2: Independent velocity time trace with 750 ns time step.
* Trace 3: Independent velocity time trace with 750 ns time step.
* Trace 4: Independent velocity time trace with 750 ns time step.
* Trace 5: Independent velocity t...

布朗运动（Brownian motion）是一种基础物理过程，其特征为热平衡（thermal equilibrium）下的均方位移（mean-squared displacement）随时间呈线性标度，该过程即人们熟知的扩散（diffusion）。在极短时间尺度下，均方位移会呈现弹道行为，即随t²标度。这一效应由爱因斯坦于1907年预言，并在近期通过实验得到观测。我们的研究表明，上述结论仅在平均意义下成立：通过对特定初始速度进行条件化处理，我们从理论上预言并经实验证实，均方位移将呈现超弹道行为，其幂律标度为t^(5/2)。该结果源于不可压缩流体（incompressible fluids）的有色噪声（colored noise），在对非零初始速度进行条件化时，热作用力（thermal force）的一阶矩（first moment）非零。这些结果为解析流体的非平衡动力学迈出了第一步。
# 液态中超弹道布朗动力学的观测
数据集DOI：[10.5061/dryad.pvmcvdnz4](10.5061/dryad.pvmcvdnz4)

## 数据与文件结构说明
我们构建了用于微流控腔（microfluidic chamber）中微球（microspheres）的光镊（optical trap）系统。我们对被捕获微球在其动量弛豫时间（momentum relaxation time）以内的位置进行了追踪，并将模拟信号（analog signal）进行数字化处理。随后，我们通过对初始速度进行条件化处理，以研究短时间尺度下的布朗运动。

### 文件与变量
#### 文件：noise_velocity.csv
**描述：** 未捕获粒子时的实验速度时间轨迹（velocity time traces），用于展示系统本底噪声，包括激光散粒噪声（laser shot noise）与其他低频噪声源（low frequency noise sources）产生的噪声。
##### 变量
* 轨迹1：独立速度时间轨迹，时间步长为750 ns。
* 轨迹2：独立速度时间轨迹，时间步长为750 ns。
* 轨迹3：独立速度时间轨迹，时间步长为750 ns。
* 轨迹4：独立速度时间轨迹，时间步长为750 ns。
* 轨迹5：独立速度时间轨迹，时间步长为750 ns。