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Main Authors: Thumann, Michael C., Boynewicz, Jason, Procopio, Giuseppe, Giona, Massimiliano, Raizen, Mark G.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.16252
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author Thumann, Michael C.
Boynewicz, Jason
Procopio, Giuseppe
Giona, Massimiliano
Raizen, Mark G.
author_facet Thumann, Michael C.
Boynewicz, Jason
Procopio, Giuseppe
Giona, Massimiliano
Raizen, Mark G.
contents The classical Einstein-Langevin theory of Brownian motion assumes a memoryless thermal bath, establishing a universal fractal dimension of $d_v = 3/2$ for the velocity fluctuations of a particle. In this Letter, we demonstrate experimentally and theoretically that fluid-inertial memory effects fundamentally redefine the fractal scaling of these fluctuations. In analyzing highly resolved measurements of Brownian microspheres in liquids, we show that the non-Markovian hydrodynamic thermal noise establishes a distinct velocity fractal dimension of $d_v = 7/4$. Coupled with theoretical analysis of non-equilibrium short-time dynamics and the initial scaling of the velocity autocorrelation function, this result establishes the non-equilibrium universality class of Brownian motion in fluid media possessing a finite non-vanishing density.
format Preprint
id arxiv_https___arxiv_org_abs_2605_16252
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The fractal dimension of Brownian dynamics in liquids
Thumann, Michael C.
Boynewicz, Jason
Procopio, Giuseppe
Giona, Massimiliano
Raizen, Mark G.
Statistical Mechanics
The classical Einstein-Langevin theory of Brownian motion assumes a memoryless thermal bath, establishing a universal fractal dimension of $d_v = 3/2$ for the velocity fluctuations of a particle. In this Letter, we demonstrate experimentally and theoretically that fluid-inertial memory effects fundamentally redefine the fractal scaling of these fluctuations. In analyzing highly resolved measurements of Brownian microspheres in liquids, we show that the non-Markovian hydrodynamic thermal noise establishes a distinct velocity fractal dimension of $d_v = 7/4$. Coupled with theoretical analysis of non-equilibrium short-time dynamics and the initial scaling of the velocity autocorrelation function, this result establishes the non-equilibrium universality class of Brownian motion in fluid media possessing a finite non-vanishing density.
title The fractal dimension of Brownian dynamics in liquids
topic Statistical Mechanics
url https://arxiv.org/abs/2605.16252