Dynamics of 1D and 3D quantum droplets in parity-time-symmetric harmonic-Gaussian potentials with two competing nonlinearities

In this paper, we investigate stable quantum droplet (alias soliton) propagations in the one-and three-dimensional (1D and 3D) amended Gross-Pitaevskii equations (alias nonlinear Schrodinger equations) with two competing nonlinearities and PT-symmetric harmonic-Gaussian potentials. Especially, in the 1D case, we demonstrate that the PT potential can admit fully-real linear spectra in certain potential parameter region, with apparent PT symmetry breaking behaviors. And, the stabilities of exact and numerical solitons are investigated. It can be found that the stabilities of solitons depend on not only the gain-and-loss strength (the condensate norm) but also the chemical potential. Then the relationship between two competing nonlinearities is adjusted by changing the strength of nonlinearity. It is concluded that the Lee-Huang-Yang (LHY) correction plays an active role in droplet stabilization Furthermore, collisions between solitons with unequal norms are explored in the PT potential in detail, and there exist elastic collisions for certain parameters. And the strong LHY correction term will ensure the stable dynamical behaviors of the droplets. Finally, we explore the excitation initialized by density-modulation and find that some excited droplets can propagate like breathers. And the adiabatic excitations by changing the potential parameters and strength of the cubic nonlinearity are also discussed. These results will have the implication for understanding the relevant quantum droplet phenomena and designing the related experiments.(c) 2022 Elsevier B.V. All rights reserved.