Excitations and phase segregation in a two-component Bose-Einstein condensate with an arbitrary interaction

Bogoliubov-de Gennes equations and the excitation spectrum of a two-component Bose-Einstein condensate (BEC) are derived with an arbitrary interaction between bosons, including long-range and short-range forces. Spectra of optical and acoustic plasmons (APs) are obtained. For the Coulomb interaction the AP has a quadratic long-wavelength dispersion in contrast with the linear dispersion in the normal-state two-component plasma. The nonconverting BEC mixture segregates into two phases for some two-body interactions. Gross-Pitaevskii equations are solved for the phase-segregated BEC. A possibility of boundary-surface and other localized excitations is studied.