 Uniform ring condensate

A one-dimensional condensate on a ring of circumference $2\pi R$ has a uniform winding state $\psi =\sqrt{N/(2\pi R)}{e}^{in\theta }$ when the order parameter is normalized to atom number. Its angular momentum per atom is $n\hslash$, while the flow contribution to its total chemical potential is ${\hslash }^2{n}^2/(2m{R}^2)$.