Lorentz forces induce inhomogeneity and flux in active systems

Abstract

We consider the nonequilibrium dynamics of a charged active Brownian particle in the presence of a space dependent magnetic field. It has recently been shown that the Lorentz force induces a particle flux perpendicular to density gradients, thus preventing a diffusive description of the dynamics. Whereas a passive system will eventually relax to an equilibrium state, unaffected by the magnetic field, an active system subject to a spatially varying Lorentz force settles into a nonequilibrium steady state characterized by an inhomogeneous density and divergence-free bulk fluxes. A macroscopic flux of charged active particles is induced by the gradient of the magnetic field only and does not require additional symmetric breaking such as density or potential gradients. This stands in marked contrast to similar phenomena in condensed matter such as the classical Hall effect. In a confined geometry we observe circulating fluxes, which can be reversed by inverting the direction of the magnetic field. Our theoretical approach, based on coarse-graining of the Fokker-Planck equation, yields analytical results for the density, fluxes, and polarization in the steady state, all of which are validated by direct computer simulation. We demonstrate that passive tracer particles can be used to measure the essential effects of the Lorentz force on the active particle bath, and we discuss under which conditions the effects of the flux could be observed experimentally.arXiv:1908.02577v1 [cond-mat.soft]

Generalized Fluctuation-Dissipation relations holding in non-equilibrium dynamics

“…Even if many experimental systems of active matter have microscopic sizes [21] and usually move in environments with large viscosity (in such a way that inertial forces are negligible), recently, the effects of inertia [66] have been highlighted in many experimental active systems, such as vibro-robots [67], Hexbug crawlers and camphor surfers [68] and vibration-driven granular particles [69][70][71] (in the granular case, the response function has been also calculated experimentally [72]). To include the active force in these physical systems, the active Langevin model has been introduced [66,67,[73][74][75][76] so that the equation of motion of the active particle is described by its position, x, and velocity, v:…”

Non-equilibrium, weak-field induced magnetism: a mechanism for magnetobiology

“…Another pertinent topic is to incorporate electrostatic interactions between the ions that are neglected here. Further research can establish relations of our results with active matter under magnetic field [43], electromagnetic noise [23,45], and nanomagnetic particles [59].…”

“…Equations similar to (2.1), i.e. Langevin equations with magnetic field, were studies at many places in application to plasma physics or stochastic systems [22,23,24,27,40,41,42,43]; see especially [25,44,45,46]. Our focus will be on implications of (2.1) for magnetobiology, i.e.…”

“…( 5.2) belongs to the class of linear oscillators driven subject to non-local friction and noise. Such systems were studied in [24,25,27,40,41,42,43,44,54,55,56,57]. We apply Fourier's transform to ζ and ξ in (5.2):…”

Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force

“…The antisymmetric part of the correlation matrix plays a crucial role for featuring nonequilibrium-ness in this subtle overdamped limit, which generates a rotational probability current (curl flux), verified recently by numerical simulations for various systems [42][43][44][45]. This can be more transparent by deriving the probability current directly in the Fokker-Planck description.…”