Analogue of the quantum Hall effect for neutral particles with magnetic dipole moment

In this paper we investigate a possibility for the existence of an analog of the Quantum Hall Effect for neutral particles with a permanent magnetic moment $\mu$ in the presence of crossed inhomogeneous magnetic and electric fields. We predict the appearance of Hall conductivity $\sigma_H=(e^2/h)\nu (\mu)$ with the Landau filling factor $\nu (\mu)\propto \mu ^2$. The estimates of the model parameters suggest quite an optimistic possibility to experimentally verify this prediction in optically trapped clouds of atomic BEC.