Non-Integral Nonlinear Schrödinger Equation for Polarized Ultracold Fermions: Spectrum of Collective Excitations

Abstract

A non-integral nonlinear Schrodinger equation for polarized fermions is proposed. Peculiarities of this equation for atoms with an electric and a magnetic dipole moment are discussed. The corresponding equations of quantum hydrodynamics are presented. Maxwell’s equations are used to describe the electromagnetic field created by the dipoles. The dispersion of linear collective excitations is obtained for polarized fermions. A comparison is made with the spectrum of collective excitations of the polarized Bose–Einstein condensates. A derivation of the equations from the microscopic theory is not considered; however, the equations proposed in this work can be obtained from microscopic quantum theory by the method of quantum hydrodynamics.