The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ``puddles'' with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
Recently bosonic quantum Hall droplets have been observed in rapidly rotating two-dimensional Bose-Einstein condensates (BECs), which exhibit robust dynamical stability. Inspired by this, we systematically investigate the collision and coalescence dynamics of these droplets within the Gross-Pitaevskii framework. For two-droplet collisions, we find two distinct collision outcomes, namely merging and separation, that are controlled by the initial relative velocity. The critical velocity exhibits a universal scaling law with the interaction and the particle number as
vc∝(gN)1/4, which can be interpreted from a simplified analytical model, revealing the essential role of the collision time. It differs fundamentally from the mechanism governing the conventional Lee-Huang-Yang stabilized quantum droplets. Furthermore, while the collision can change the shape of the droplet significantly, the center of mass trajectory remains nearly unaffected, owing to the conservation of angular momentum. For overlapping stationary droplets, vortex arrays can emerge through Kelvin-Helmholtz instability driven by phase-induced shear flow. Although two droplets may merge into a larger one, extended states cannot be constructed from multiple overlapping droplets. Instead, the system dynamically reorganizes into new isolated droplets, revealing the localized property in the bulk region. Our results reveal the unique nonequilibrium dynamics of quantum Hall droplets and suggest new pathways for manipulating strongly correlated rotating quantum fluids.
We use exact quantum Monte Carlo techniques to study the properties of quantum droplets in two-component bosonic mixtures with contact interactions in one spatial dimension. We systematically study the surface tension, the density profile and the breathing mode as a function of the number of particles in the droplet and of the ratio of coupling strengths between intraspecies repulsion and interspecies attraction. We find that deviations from the predictions of the generalized Gross-Pitaevskii equation are small in most cases of interest.
A quantum droplet is a self-bound state balanced by the mean-field interaction and Lee–Huang–Yang correction in a Bose–Bose mixture. In this paper, we study the collisional dynamics of two-dimensional quantum droplets with a vortex. By adjusting the initial momentum, the initial phase difference, the topological charge of the quantum droplets, and the total number of particles, we identify three dynamic mechanisms of collisions, namely, splitting, no-splitting, and their crossover according to the states after collision, which are significantly different from the merging, separation, and evaporation of the collisional dynamics of vortex-free droplets. The initial phase difference of the two droplets changes the interference fringes and the manner of splitting of the droplets. We also show that the three-body loss of atoms does not affect the result.
We investigate the dynamics of Bose-Einstein condensate droplets composed of
164Dy atoms formed in a double-well potential following removal of the interwell barrier. By solving the dipolar Gross-Pitaevskii equation, we determine phase diagrams of ground-state configurations as functions of the atom number confined in the double-well potential. For an interwell separation
2d=3μm, we consider the relative dipolar-to-contact interaction strengths
εdd=1.4,
1.45, and
1.5. Symmetry-broken lowest-energy configurations are found for
εdd=1.5 and, over a reduced range of atom numbers, for
εdd=1.45, whereas no symmetry-broken states are found for
εdd=1.4 up to
N=5×104. We analyze the subsequent time evolution after removal of the central barrier, revealing both droplet oscillations and merger events leading to the formation of larger droplets. The oscillations are driven by the external potential and by the repulsive tails of the in-plane component of the dipolar interaction. For the two-droplet states at
εdd=1.5 and
2d=3μm, merging is found for
N=8000 and
8800, whereas the droplets remain separated for the investigated cases with
N≥9000. Increasing the initial separation to
2d=5μm shifts the approximate upper atom number for merging to
N≃1.65×104, demonstrating that the crossover is controlled by the competition between the post-quench excess energy and the repulsive inter-droplet barrier.
We derive a channel-resolved Lee-Huang-Yang correction and construct an extended GrossPitaevskii model for one-dimensional polar spin-1 quantum droplets. The fluctuation contribution separates into density and spin channels, which supports self-bound droplets even when the spinindependent mean-field interaction is repulsive. Stationary solutions exhibit a continuous crossover from soliton-like to flat-top droplets, accompanied by saturation of the chemical potential and peak density as the particle number increases. Within the parameter range examined here, linear Bogoliubov analysis together with weak-perturbation dynamics supports the stability of both droplet types. A quadratic-Zeeman quench reveals a finite-size crossover in breathing dynamics and distinct nonequilibrium roles of the density and spin fluctuation channels. Representative head-on collisions further show that the finite-size crossover modulates phase-sensitive nonlinear scattering, with in-phase impact producing coalescence-like central retention and out-of-phase impact favoring quasi-elastic separation. The analysis clarifies how density and spin fluctuations shape equilibrium structure and nonequilibrium response in low-dimensional polar spinor droplets.