Scale-free correlations are believed to be generic in out of equilibrium systems but their explicit derivations are rare and often involve approximations. Here we analyze a system of infinitely persistent active Brownian particles in the low density and small-swim-velocity limit. We show that both the density and swim velocity correlations decay algebraically as r^{-(d+1)} (with logarithmic corrections in d=2). In reciprocal space these correlations manifest themselves as cusps at k=0. The analytical predictions are confirmed by numerical simulations. The results were obtained through interaction with Claude (Opus 4.8 and 5, and Fable 5) and verified by the author.
We develop a spectral theory for dynamical large deviations in non-Markov jump processes and non-Markov chains, whose dynamics depends on the past through state- and jump-dependent empirical observables. We demonstrate that a multiscale Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) Ansatz separates fast configurational rel...
The Ballistic Macroscopic Fluctuation Theory (BMFT) is a path-integral based approach to treat large-scale correlations in interacting integrable systems which, so far, has only been applied to quasi-equilibrium settings. In this paper we extend this approach to integrable quench problems and, to illustrate it, we comp...
We investigate the statistics of the time-integrated current in an infinite one-dimensional gas of independent active Ornstein--Uhlenbeck particles, as a model system for studying an active generalisation of the corresponding passive (diffusive) phenomenology. Unlike the latter, where current fluctuations exhibit unive...
Sandeep Jangid, Aman Kumbhakar, Juliane U. Klamser et al.· 0 citations
We study the off-diagonal matrix elements of real-space observables in time-reversal-invariant single-particle chaotic systems. By analyzing the semiclassical expression for the off-diagonal variance derived from Berry's conjecture, we show that the banded structure of the observable matrix emerges naturally. For local...
The pace of evolution depends on how rapidly new phenotypes arise. We show that neutral Wright-Fisher evolution exhibits anomalous first passage despite diffusive mutations. The mean time for the first individual to reach a prescribed phenotypic distance scales approximately as $(\sigma^2)^{-3/2}$ with mutation varianc...
Tetsuhiro S. Hatakeyama· 0 citations
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