DOI: 10.5061/dryad.pvmcvdnz4
title: Observation of super-ballistic Brownian dynamics in liquid

description: 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.
description: # 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 time trace with 750 ns time step. #### File:
 noise_position.csv **Description:** Experimental position 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 position time trace with 750 ns time step. * Trace
 2: Independent position time trace with 750 ns time step. * Trace
 3: Independent position time trace with 750 ns time step. * Trace
 4: Independent position time trace with 750 ns time step. * Trace
 5: Independent position time trace with 750 ns time step. #### File:
 barium_titanate_in_acetone_velocity.csv **Description:** Experimental
 velocity time trace for optically trapped microsphere. ##### 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 time trace with 750 ns time step. #### File:
 barium_titanate_in_acetone_position.csv **Description:** Experimental
 position time trace for optically trapped microsphere. ##### Variables *
 Trace 1: Independent position time trace with 750 ns time step. * Trace
 2: Independent position time trace with 750 ns time step. * Trace
 3: Independent position time trace with 750 ns time step. * Trace
 4: Independent position time trace with 750 ns time step. * Trace
 5: Independent position time trace with 750 ns time step. #### File:
 fitting.ipynb **Description:** File contains the code that is used to fit
 the hydrodynamic theory to the equilibrium MSD data. We use a fixed barium
 titanate density and find the average radius, trap strength, and
 volts/meter conversion between the fits on the MSDs from the five
 independent time traces. #### File: conditioning.ipynb
 **Description:** File contains the code used to condition data and compare
 to theory. Functions directly corresponding to equations from the text are
 compared to conditioned MSDs. ## Code/software All of the scripts can be
 run inside a python environment with standard packages. The raw data is
 loaded into the fitting file that outputs processed time traces. These
 time traces are the data files provided. These can then be put into the
 conditioning file to extract conditioned MSDs. ## Access information Other
 publicly accessible locations of the data: * none Data was collected in
 the experimental Raizen lab at the University of Texas at Austin