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We investigate the effects of higher-order quantum fluctuations on the bulk properties of self-bound droplets in three-, two- and one-dimensional binary Bose mixtures using the Hartree–Fock–Bogoliubov theory. We calculate higher-order corrections to the equation of state of the droplet at both zero and finite temperatures. We show that our results for the ground-state energy are in a good agreement with recent quantum Monte Carlo simulations in any dimension. Our study extends to the finite temperature case where it is found that thermal fluctuations may destabilize the droplet state and eventually destroy it. In two dimensions, we reveal that the droplet occurs at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature.

We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of weak random potential with a Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a closed set of equations that highlight the role of the spectacular interplay between the disorder and the interspecies interactions in the time evolution of the density induced by disorder in each component. It is found that this latter increases with time favoring localization of both species. The time scale at which the theory remains valid depends on the respective system parameters. We show analytically and numerically that such a system supports a steady state that periodically changing during its time propagation. The obtained dynamical corrections indicate that disorder may transform the system into a stationary out-of-equilibrium states. Understanding this time evolution is pivotal for the realization of Floquet condensates.

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