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arXiv · 2605.16252

The fractal dimension of Brownian dynamics in liquids

Michael C. Thumann·Jason Boynewicz·Giuseppe Procopio·Massimiliano Giona·Mark G. Raizen
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Abstract

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.

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Michael C. Thumann, Jason Boynewicz, Giuseppe Procopio, Massimiliano Giona, Mark G. Raizen. 2026-05-15. The fractal dimension of Brownian dynamics in liquids. https://arxiv.org/abs/2605.16252

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