Roy, ArkoArkoRoyGautam, S.S.GautamAngom, D.D.Angom2025-08-222025-08-222015-01-012331-8422http://arxiv.org/abs/1501.03590http://repository.iitgn.ac.in/handle/IITG2025/18137We show that the third Goldstone mode in the two-species condensate mixtures, which emerges at phase-separation, gets hardened when the confining potentials have separated trap centers. The {\em sandwich} type condensate density profiles, in this case, acquire a {\em side-by-side} density profile configuration. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution and density profiles for these phase transitions at T=0.en-USQuantum Gasese-Print123456789/615