Gigantic dynamical spreading and anomalous diffusion of jerky active particles
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918090163355648 |
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| author | Löwen, Hartmut |
| author_facet | Löwen, Hartmut |
| contents | Jerky active particles are Brownian self-propelled particles which are dominated by ``jerk'', the change in acceleration. They represent a generalization of inertial active particles. In order to describe jerky active particles, a linear jerk equation of motion which involves a third-order derivative in time, Stokes friction and a spring force is combined with activity modeled by an active Ornstein-Uhlenbeck process. This equation of motion is solved analytically and the associated mean-square displacement (MSD) is extracted as a function of time. For small damping and small spring constants, the MSD shows an enormous superballistic spreading with different scaling regimes characterized by anomalous high dynamical exponents 6, 5, 4 or 3 arising from a competition between jerk, inertia and activity. When exposed to a harmonic potential, the gigantic spreading tendency induced by jerk gives rise to an enormous increase of the kinetic temperature and even to a sharp localization-delocalization transition, i.e. a jerky particle can escape from harmonic confinement. The transition can be either first or second order as a function of jerkiness. Finally it is shown that self-propelled jerky particles governed by the basic equation of motion can be realized experimentally both in feedback-controlled macroscopic particles and in active colloids governed by friction with memory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gigantic dynamical spreading and anomalous diffusion of jerky active particles Löwen, Hartmut Soft Condensed Matter Jerky active particles are Brownian self-propelled particles which are dominated by ``jerk'', the change in acceleration. They represent a generalization of inertial active particles. In order to describe jerky active particles, a linear jerk equation of motion which involves a third-order derivative in time, Stokes friction and a spring force is combined with activity modeled by an active Ornstein-Uhlenbeck process. This equation of motion is solved analytically and the associated mean-square displacement (MSD) is extracted as a function of time. For small damping and small spring constants, the MSD shows an enormous superballistic spreading with different scaling regimes characterized by anomalous high dynamical exponents 6, 5, 4 or 3 arising from a competition between jerk, inertia and activity. When exposed to a harmonic potential, the gigantic spreading tendency induced by jerk gives rise to an enormous increase of the kinetic temperature and even to a sharp localization-delocalization transition, i.e. a jerky particle can escape from harmonic confinement. The transition can be either first or second order as a function of jerkiness. Finally it is shown that self-propelled jerky particles governed by the basic equation of motion can be realized experimentally both in feedback-controlled macroscopic particles and in active colloids governed by friction with memory. |
| title | Gigantic dynamical spreading and anomalous diffusion of jerky active particles |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2507.08910 |