Evolutionary Dynamics Of Multidimensional Quantum Droplets

The existence of self-bound local quantum states in cold atomic systems is a hot topic and an important branch of nonlinear physics.The discovery of quantum droplets in two-component Bose-Einstein condensates is the latest development in recent years.This self-bound state is stabilized by self-repulsion induced by quantum fluctuations around the mean field,known as the Lee-Huang-Yang effect.The theoretical model describing the distribution state of atoms is the GrossPitaevskii equation modified by Lee-Hwang-Yang,and the model also makes specific processing for quantum droplets of different dimensions.For example,the cubic mean field attraction term and the quadric repulsion term induced by LHY are used to describe the inter-component attraction and intra-group repulsion of the competitive nonlinear three-dimensional droplet,and the competitive term is represented by the cubic term multiplied by the logarithmic factor when describing the two-dimensional droplet.The potential application value of this new form of matter is reflected in the future quantum information processing and interference measurement of matter waves.The whole paper is mainly developed with two dimensional and three dimensional frames.The evolution characteristics of vortex quantum droplets disturbed by internal modes are discussed in two dimensions.The angular dependent internal modes and their eigenvalues of basic and vortex droplets with different topological charges are solved.When the internal mode corresponding to the maximum eigenvalue is excited,the perturbed droplet deforms and presents a regular polygon structure.The neutral internal mode allows the droplet to evolve like respiration,i.e.the effective width behaves as a whole oscillating over time.The internal mode with higher angular index will lead to continuous periodic rotation of the droplet,and the relationship between rotation period and oscillation period is related to the topological charges.The existence and stability of multipole quantum droplet clusters are investigated in three dimensions,and the existence intervals of dipole,quadrupole and octupole quantum droplet clusters are obtained by solving the corresponding nonlinear Schrodinger equation numerically.Moreover,the solution of droplet clusters with more poles is also investigated.With the increase of the number of droplet poles,the relative distance between pearls becomes smaller,and the trend of radial expansion and angular extrusion occurs.The size of individual pearls increases with the increase of power.Through numerical evolution simulation,it is found that the structure and distribution remain relatively stable for a long time.Even if unstable structural failure occurs,it will occur after a long evolution time.