 Two-component Bose-Einstein condensate

Two separately conserved bosonic species have two condensate fields and independent chemical potentials. A contact interaction energy density $U_{11}{n}_1^2/2+U_{22}{n}_2^2/2+U_{12}{n}_1{n}_2$ gives ${\mu }_1=U_{11}{n}_1+U_{12}{n}_2$ and ${\mu }_2=U_{12}{n}_1+U_{22}{n}_2$ in a uniform mixture. Coherent interconversion would change the conservation constraints and cannot be included while retaining independent particle-number constraints unchanged.