ﻻ يوجد ملخص باللغة العربية
A recent analysis has revealed singular but physically relevant 2D localized vortex states with density ~ 1/r^{4/3} at r --> 0 and a convergent total norm, which are maintained by the interplay of the potential of the attraction to the center, ~ -1/r^2, and a self-repulsive quartic nonlinearity, produced by the Lee-Huang-Yang correction to the mean-field dynamics of Bose-Einstein condensates. In optics, a similar setting, with the density singularity ~ 1/r, is realized with the help of quintic self-defocusing. Here we present physically relevant antidark singular-vortex states in these systems, existing on top of a flat background. Numerical solutions for them are very accurately approximated by the Thomas-Fermi wave function. Their stability exactly obeys an analytical criterion derived for small perturbations. It is demonstrated that the singular vortices can be excited by the input in the form of ordinary nonsingular vortices, hence the singular modes can be created in the experiment. We also consider regular (dark) vortices maintained by the flat background, under the action of the repulsive central potential ~ +1/r^2. The dark modes with vorticities l = 0 and l = 1 are completely stable. In the case when the central potential is attractive, but the effective one, which includes the centrifugal term, is repulsive, and a weak trapping potential ~ r^2 is added, dark vortices with l = 1 feature an intricate pattern of alternating stability and instability regions. Under the action of the instability, states with l = 1 travel along tangled trajectories, which stay in a finite area defined by the trap. The analysis is also reported for dark vortices with l = 2, which feature a complex structure of alternating intervals of stability and instability against splitting. Lastly, simple but novel flat vortices are found at the border between the anidark and dark ones.
This article provides a focused review of recent findings which demonstrate, in some cases quite counter-intuitively, the existence of bound states with a singularity of the density pattern at the center, while the states are physically meaningful be
We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations of the un
Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only rec
Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons with the main emphasis on the possibility to trap them on top of a pedestal-shaped po
We study the out-of-equilibrium dynamics of a two-dimensional paraxial fluid of light using a near-resonant laser propagating through a hot atomic vapor. We observe a double shock-collapse instability: a shock (gradient catastrophe) for the velocity,