Stability of two-component Bose-Einstein condensates in traps

Static and dynamic stabilities of two-component Bose-Einstein condensates t rapped in harmonic potentials are studied. Using the variational method, we obtain the static stability condition and the phase separation condition. They are expressed as functions of the particle numbers and the s-wave scat tering lengths. We find that the interaction between the different species of atoms (simply, interspecies interaction) has significant effects on the stability of Each condensate. The instability of the ground state is explai ned in terms of the low-lying (softening) of the collective excitation ener gies. We investigate thr low-lying excitations and the possibility of their softening by use of thr Gaussian ansatz and the sum-rule approach.