Paramagnetism in spherically confined charged active matter

TL;DR

This paper demonstrates that classical charged active particles confined on a sphere exhibit a nonzero paramagnetic magnetization, contrasting with traditional equilibrium systems, supported by numerical and analytical analysis.

Contribution

It reveals that classical charged active matter can have a paramagnetic response, challenging the classical theorem that forbids magnetization in thermal equilibrium.

Findings

Classical charged active particles show nonzero magnetization.

Numerical simulations agree with analytical solutions of the Fokker-Planck equation.

The system exhibits a paramagnetic response contrary to classical expectations.

Abstract

The celebrated theorem of Bohr and van Leeuwen guarantees that a classical charged system cannot have a magnetization in thermal equilibrium. Quantum mechanically, however, a diamagnetic response is obtained. In contrast, we show here that a classical charged active system, consisting of a motile particle confined to the surface of a sphere, has a nonzero magnetization and a paramagnetic response. We numerically sample Langevin trajectories of this system and compare with limiting analytical solutions of the Fokker-Planck equation, at small and large temperatures, to find excellent agreement in the magnetic response. Our Letter suggests experimental routes to controlling and extracting work from charged active matter.