We study the collective modes of a binary Bose mixture across the soliton to
droplet crossover in a quasi one dimensional waveguide with a beyond-mean-field
equation of state and a variational Gaussian ansatz for the scalar bosonic
field of the corresponding effective action. We observe a sharp difference in
the collective modes in the two regimes. Within the soliton regime modes vary
smoothly upon the variation of particle number or interaction strength. On the
droplet side collective modes are inhibited by the emission of particles. This
mechanism turns out to be dominant for a wide range of particle numbers and
interactions. In a small window of particle number range and for intermediate
interactions we find that monopole frequency is likely to be observed. In the
last part we focus on the spin-dipole modes for the case of equal intraspecies
interactions and equal equilibrium particle numbers in the presence of a weak
longitudinal confinement. We found that such modes might be unobservable in the
real-time dynamics close to the equilibrium as their frequency is higher than
the particle emission spectrum by at least one order of magnitude in the
droplet phase. Our results are relevant for experiments with two-component BECs
for which we provide realistic parameters.Comment: Accepted for Publication in PR
