Kuriatnikov Y. Nonlinear dynamics of toroidal Bose-condensates.

This thesis is devoted to the theoretical study of the nonlinear dynamics of toroidal Bose condensates of atomic gases and axion dark matter with a focus on the generation and decay of persistent currents via vortex interaction and the study of their stability. Experimental studies of Bose-Einstein condensates of atomic gases have started over thirty-five years ago. Experimental physics is actively working on the study of phenomena related to superfluidity. The study of persistent currents is one of the directions of these studies. Recently numerous experiments have been studying persistent currents in Bose-Einstein condensates (BECs) trapped in a ring geometry. Experiments with ultracold gases open up amazing opportunities for fundamental research of the superfluidity phenomenon, which can be used to make high-precision metrology devices. In the first chapters of this work we analyze nonlinear dynamics of Bose-Einstein condensate trapped in a toroidal trap which is driven by a wide repulsive laser beam that rotates slowly along the ring, forming a localized region of the reduced density also called as a "weak link". Such a system is interesting for research, because of analogy with a superconducting circuit with a Josephson contact, it can act as a nonlinear interferometer. The high sensitivity of the condensate’s phase to the angular frequency of the wide laser is similar to the sensitivity of the superconducting current in a superconducting quantum interferometer to changes in the external magnetic field. Bose condensates might be used for future developments of highly sensitive devices for measuring angular frequencies. But this requires accurate models that numerically reproduce the qualitative and quantitative characteristics of the experiment. We chose physical parameters for numerical modeling of 8 studied systems with the aim to have the most accurate reproduction of experiments. In the mean field approximation, we simulated condensate dynamics modeling the experiment. Numerically and analytically studied conditions for the generation and decay of persistent currents in Bose-condensates trapped in toroidal traps. Even though condensate is a macroscopic quantum system of tens or even hundreds of microns in size, quantum vortices are smaller than a micron. To detect vortices, condensate is observed milliseconds after releasing from the trap. Here theoretical models help to study in details the physical processes happening in the experiment.