The Countoscope for self-propelled particles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914447453323264 |
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| author | Cerdin, Tristan Calazans, Talia Douarche, Carine Marbach, Sophie |
| author_facet | Cerdin, Tristan Calazans, Talia Douarche, Carine Marbach, Sophie |
| contents | Particle number fluctuations $N(t)$, measured in virtual observation boxes of an image or a simulation, offer a way to quantify particle dynamics when particle tracking is impractical, such as in high-density systems. While traditionally limited to equilibrium diffusive systems, we extend this approach -- named ``Countoscope'' -- to out-of-equilibrium self-propelled particles: Active Brownian (ABPs), Run and Tumble (RTPs), and Active Ornstein-Uhlenbeck Particles (AOUPs). For AOUPs, we leverage their Gaussian statistics to derive a general formula applicable to any Gaussian system. For ABPs and RTPs, we derive the intermediate scattering function (ISF) -- and thus the correlations of $N(t)$ -- using an exact perturbative expansion over the probability density fields, revealing key physical features of the ISF and of the number correlations. Our theoretical predictions for the mean-squared number difference $\langle ΔN^2(t) \rangle = \langle (N(t) - N(0))^2 \rangle$ match stochastic simulations and exhibit three time-dependent scaling regimes: diffusive, advective, and long-time enhanced diffusive, reflecting the regimes of the mean squared particle displacement. We further uncover limiting laws in each of these regimes that are useful to quantify self-propulsion properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02907 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Countoscope for self-propelled particles Cerdin, Tristan Calazans, Talia Douarche, Carine Marbach, Sophie Soft Condensed Matter Statistical Mechanics Particle number fluctuations $N(t)$, measured in virtual observation boxes of an image or a simulation, offer a way to quantify particle dynamics when particle tracking is impractical, such as in high-density systems. While traditionally limited to equilibrium diffusive systems, we extend this approach -- named ``Countoscope'' -- to out-of-equilibrium self-propelled particles: Active Brownian (ABPs), Run and Tumble (RTPs), and Active Ornstein-Uhlenbeck Particles (AOUPs). For AOUPs, we leverage their Gaussian statistics to derive a general formula applicable to any Gaussian system. For ABPs and RTPs, we derive the intermediate scattering function (ISF) -- and thus the correlations of $N(t)$ -- using an exact perturbative expansion over the probability density fields, revealing key physical features of the ISF and of the number correlations. Our theoretical predictions for the mean-squared number difference $\langle ΔN^2(t) \rangle = \langle (N(t) - N(0))^2 \rangle$ match stochastic simulations and exhibit three time-dependent scaling regimes: diffusive, advective, and long-time enhanced diffusive, reflecting the regimes of the mean squared particle displacement. We further uncover limiting laws in each of these regimes that are useful to quantify self-propulsion properties. |
| title | The Countoscope for self-propelled particles |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2604.02907 |