Active Ornstein-Uhlenbeck particles retain a Brownian f^{-2} spectrum in free space with a persistence-frequency crossover, while confinement produces a two-plateau structure from double trapping and an f^{-4} regime from ballistic transients.
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Quantum active matter shows mean-squared displacement scaling as t^6 or t^7 derived analytically from a Wigner phase-space master equation.
Candidate-dependent extremal alignment in topological active matter generates self-confined, spatially structured flocks by factorizing decision utility into average score times neighbor count.
Number fluctuation signals N(t) distinguish self-propelled particle models via differences in reorientation dynamics.
Exact solution for anisotropic mobility in trapped self-propelled particles yields non-monotonic negative excess kurtosis and a strictly sub-Gaussian steady-state distribution that displaces the particle into high-potential regions.
Mapping spatial motility variations to stochastic switching allows analytical prediction of diffusion and density patterns for delayed active colloids, matching experiments across scales.
Wedge confinement changes the magnitude and direction of a self-diffusiophoretic particle's velocity through reflected concentration fields in the far-field limit.
Bath memory reshapes transport patterns in the extended phase of the AAH transition but mainly renormalizes timescales in the localized phase.
An inertial chiral active Brownian particle confined in a harmonic potential transitions from Gaussian to platykurtic position distribution when harmonic and chiral frequencies match, confirmed by kurtosis dip and non-monotonic MSD.
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Power spectral density of trajectories of active Ornstein-Uhlenbeck particles
Active Ornstein-Uhlenbeck particles retain a Brownian f^{-2} spectrum in free space with a persistence-frequency crossover, while confinement produces a two-plateau structure from double trapping and an f^{-4} regime from ballistic transients.
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Mobility Anisotropy Reshapes Self-Propelled Motion
Exact solution for anisotropic mobility in trapped self-propelled particles yields non-monotonic negative excess kurtosis and a strictly sub-Gaussian steady-state distribution that displaces the particle into high-potential regions.
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Universal transport of active colloids with sensory delay in motility landscapes
Mapping spatial motility variations to stochastic switching allows analytical prediction of diffusion and density patterns for delayed active colloids, matching experiments across scales.