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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16252 |
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| _version_ | 1866911689212952576 |
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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 |