On microscopic theory of spin-S Bose-Einstein condensate in a magnetic field

TL;DR

This paper extends the Bogoliubov model to describe spin-S Bose-Einstein condensates in a magnetic field, deriving an order parameter equation and analyzing the stability and collective excitations at near-zero temperature.

Contribution

It introduces a microscopic theoretical framework for spin-S BECs in magnetic fields, including an explicit order parameter equation and stability analysis.

Findings

Derived the order parameter equation for spin-S BEC in magnetic field

Identified a solution corresponding to definite spin projection BEC

Analyzed thermodynamic stability and collective modes

Abstract

The Bogoliubov model for weakly interacting Bose gas is extended to Bose-Einstein condensation (BEC) of spin-S atoms in a magnetic field. Equation for the vectorial order parameter valid at temperature $T\to 0$ is derived and its particular solution is found. This solution corresponds to the formation of BEC of atoms with a definite spin projection onto direction of a magnetic field. We study the thermodynamic stability of the found solution and obtain the expressions for low-lying collective modes.