Dynamic effects of external axion fields in a system of many particles with spin

TL;DR

This work addresses how external pseudoscalar axion fields influence the non-relativistic collective dynamics of spinful particles in a rotating frame. Starting from the Dirac equation, the authors perform a Foldy-Wouthuysen transformation to obtain a Pauli-Schrödinger Hamiltonian that includes spin-axion and spin-rotation couplings. Using many-particle quantum hydrodynamics, they derive a closed set of balance equations for spin density and current density, incorporating axion gradients, time variations, and inertial forces. The resulting framework reveals novel torques and force densities arising from axion interactions, offering a theoretical foundation for experimental searches of axion-like dark matter through spin- and current-based observables.

Abstract

We develop the theoretical model that describes dynamic non-equilibrium effects of external inertial and axion fields in a system of particles with spin. The possibility of using the spin density and the current density of non-relativistic quantum particle systems for the detection of the hypothetical axion-like dark matter is discussed. The resulting closed system of dynamic equations encompasses the continuity equation, the momentum balance equation, and the spin density evolution equation, accounting for the influence of the spin-rotation coupling and the external axion fields. The new formalism opens up new perspectives for an experimental search of dark matter axions.