Yakimenko A.I.


Dynamics of spatial structures in nonlinear media
01.04.02 – theoretical physics
Doctor of Science Degree (Physics and Mathematics)

This habilitation thesis is devoted to the study of the wave structures in atomic Bose-Einstein condensates (BEC), nonlinear optical media and non-equilibrium plasmas.
It is revealed that spatially localized vortex solitons become stable in self-focusing nonlinear media when the vortex symmetry-breaking azimuthal instability is eliminated by a nonlocal nonlinear response. The main properties of different types of vortex beams are investigated; the physical mechanism of the vortex stabilization in spatially nonlocal nonlinear media is discussed.
Stability of multiply-charged two-dimensional bright vortex solitons in media with focusing cubic and defocusing quintic nonlinearities is investigated. It is shown that a vortex soliton becomes robust with respect to symmetry-breaking azimuthal perturbations in the self-defocusing regime above some critical beam power when its radial profile flattens. A stable high-power vortex has nearly homogeneous energy distribution across the beam with a rather sharp boundary. The dynamics of a slightly perturbed stable vortex soliton is found to be similar to the oscillations of a liquid stream having a surface tension. The explanation of stabilization of vortex solitons in media with competing nonlinearities based on the idea of sustaining effective surface tension is proposed.
Deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate are investigated. These phase slips are induced by vortex excitations created by a rotating weak link. The influence of localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate are analyzed. The dynamics of the stirred condensate far beyond the experimentally explored region is considered, surprising manifestations of complex vortex dynamics are revealed.
A hysteresis effect in the process of generation and decay of the persistent current is theoretically investigated in a toroidal BEC, driven by a rotating weak link. Using dissipative mean-field approach, it is shown, that both generation and decay of the persistent current are driven by dynamics of the moving vortex dipoles.
Stability of persistent flow in spinor Bose-Einstein condensates is studied in the framework a dissipative mean field theory. It is found that in a BEC with a dominant population in one spin component, persistent currents are stable for over two minutes. Increasing the population of atoms in a second spin component, it is observed that at a rather well-defined critical population imbalance the persistent flow becomes unstable and quickly loses vorticity in well-defined steps. The mechanism of the persistent current decay suggested in the present work probably can be similarly observed in any multicomponent condensate with repulsive interatomic interactions and in single-component toroidal BECs with a tunable weak link.
Generation and stabilization of vortex rings in atomic Bose-Einstein condensates are investigated. A novel approach for generating vortex rings by optical tweezers (two blue-detuned optical beams forming a toroidal void in a magnetically or optically confined condensate cloud) is proposed. It is demonstrated that matter-wave vortex rings trapped within the void are energetically and dynamically stable. Theoretical findings, obtained here, suggest a possibility for the generation, stabilization, and nondestructive manipulation of quantized vortex rings in experimentally feasible trapping configurations.
Two-dimensional fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of different types are considered. The general properties of the stationary states are investigated variationally and numerically. The stability regions of the soliton-soliton pairs are determined.
The phenomenon of stable persistent currents is central to the studies of superfluidity in a range of physical systems. While most of the previous theoretical studies of superfluid flows in annular geometries concentrated on conservative systems, here is extended the dynamical stability analysis of persistent currents to open dissipative exciton-polariton superfluids. By considering an exciton-polariton condensate in an optically induced annular trap, dynamical stability conditions are determined for an initially imposed flow with a nonzero orbital angular momentum. It is shown, theoretically and numerically, that the system can sustain metastable persistent currents in a large parameter region, and describe scenarios of the supercurrent decay due to the dynamical instability.
The generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave.
One of the main candidates for the explanation of anomalous electron transport in tokamaks is the reactive trapped electron mode driven by compressibility (curvature) and electron temperature gradient. The influence of flow shear on this mode is studied by solving the radial eigenvalue problem. It is found that the Waltz rule stabilization criterion usually gives too strong a stabilization of this mode. The spatial-temporal evolution of unstable trapped electron modes is also investigated. It is found that it is strongly influenced by the continuum part of the spectrum. It is shown that the modes propagate with acceleration from the source region, thereby widening the region of instability.
Localized two- and three-dimensional Langmuir solitons are studied in the framework of model based on generalized nonlinear Schrödinger equation that accounts for local and nonlocal contributions to electron–electron nonlinearity. General properties of solitons are investigated analytically and numerically. Evolution of three-dimensional localized wave packets has been simulated numerically. The additional nonlinearities are shown to be able to stabilize both azimuthally symmetric two-dimensional and spherically symmetric three-dimensional Langmuir solitons.
Key words: soliton, vortex stability of solitons, atomic Bose-Einstein condensate, non-equilibrium plasma.

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