Spin-orbit-coupled fractional oscillators and trapped Bose-Einstein condensates.

We study the ensemble of pseudo-spin 1/2 ultracold bosons, performing Lévy flights, confined in a parabolic potential. The (pseudo-) spin-orbit coupling (SOC) is additionally imposed on these particles. We consider the structure and dynamics of macroscopic pseudospin qubits based on Bose-Einstein condensates, obtained from the above "fractional" bosons. Under "fractional" we understand the substitution of the ordinary second derivative (kinetic energy term) in the Gross-Pitaevskii equation by a so-called fractional Laplacian, characterized by the Lévy index µ. We show that the joint action of interparticle interaction, SOC, and Zeeman splitting in a synthetic magnetic field makes the dynamics of corresponding qubit highly nontrivial with evident chaotic features at both strong interactions and Lévy indices µâ†’1 when the Lévy trajectories of bosons with long jumps dominated over those derived from ordinary Gaussian distribution, corresponding to µ=2. Using analytical and numerical arguments, we discuss the possibilities to control the above qubit using the synergy of SOC, interaction strength, and "fractionality," characterized by the Lévy index µ.

Screened Coulomb interaction in insulators with strong disorder.

We study the effect of disorder on the excitons in a semiconductor with screened Coulomb interaction. Examples are polymeric semiconductors and/or van der Waals structures. In the screened hydrogenic problem, we consider the disorder phenomenologically using the so-called fractional Scrödinger equation. Our main finding is that joint action of screening and disorder either destroys the exciton (strong screening) or enhances the bounding of electron and hole in an exciton, leading to its collapse in the extreme case. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in the above semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important. Our theoretical results permit one to predict the various excitonic properties in semiconductor samples with different degrees of disorder and Coulomb interaction screenings.

1D solitons in cubic-quintic fractional nonlinear Schrödinger model.

We examine the properties of a soliton solution of the fractional Schrö dinger equation with cubic-quintic nonlinearity. Using analytical (variational) and numerical arguments, we have shown that the substitution of the ordinary Laplacian in the Schrödinger equation by its fractional counterpart with Lévy index [Formula: see text] permits to stabilize the soliton texture in the wide range of its parameters (nonlinearity coefficients and [Formula: see text]) values. Our studies of [Formula: see text] dependence ([Formula: see text] is soliton frequency and N its norm) permit to acquire the regions of existence and stability of the fractional soliton solution. For that we use famous Vakhitov-Kolokolov (VK) criterion. The variational results are confirmed by numerical solution of a one-dimensional cubic-quintic nonlinear Schrödinger equation. Direct numerical simulations of the linear stability problem of soliton texture gives the same soliton stability boundary as within variational method. Thus we confirm that simple variational approach combined with VK criterion gives reliable information about soliton structure and stability in our model. Our results may be relevant to both optical solitons and Bose-Einstein condensates in cold atomic gases.

Fractional quantum oscillator and disorder in the vibrational spectra.

We study the role of disorder in the vibration spectra of molecules and atoms in solids. This disorder may be described phenomenologically by a fractional generalization of ordinary quantum-mechanical oscillator problem. To be specific, this is accomplished by the introduction of a so-called fractional Laplacian (Riesz fractional derivative) to the Scrödinger equation with three-dimensional (3D) quadratic potential. To solve the obtained 3D spectral problem, we pass to the momentum space, where the problem simplifies greatly as fractional Laplacian becomes simply [Formula: see text], k is a modulus of the momentum vector and [Formula: see text] is Lévy index, characterizing the degree of disorder. In this case, [Formula: see text] corresponds to the strongest disorder, while [Formula: see text] to the weakest so that the case [Formula: see text] corresponds to "ordinary" (i.e. that without fractional derivatives) 3D quantum harmonic oscillator. Combining analytical (variational) and numerical methods, we have shown that in the fractional (disordered) 3D oscillator problem, the famous orbital momentum degeneracy is lifted so that its energy starts to depend on orbital quantum number l. These features can have a strong impact on the physical properties of many solids, ranging from multiferroics to oxide heterostructures, which, in turn, are usable in modern microelectronic devices.

The influence of Coulomb interaction screening on the excitons in disordered two-dimensional insulators.

We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova-Keldysh interaction by means of so-called fractional Scrödinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index [Formula: see text]) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important.

The influence of disorder on the exciton spectra in two-dimensional structures.

We study the role of disorder in the exciton spectra in two-dimensional (2D) semiconductors. These can be heterostructures, thin films and multilayers (so-called van der Waals structures) of organometallic perovskites, transition metal dichalcogenides and other semiconductors for optoelectronic applications. We model the disorder by introduction of a fractional Laplacian (with Lévy index µ, defining the degree of disorder) to the Scrödinger equation with 2D Coulomb potential. Combining analytical and numerical methods, we observe that the exciton exists only for µ > 1, while the point µ = 1 (strongest disorder) corresponds to the exciton collapse. We show also that in the fractional (disordered, corresponding to 1 < µ < 2; µ = 2 corresponds to the ordered case) 2D hydrogenic problem, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number n but also on orbital m. These features can have a profound influence on the lifetime of optically generated excitons in the above 2D semiconductor structures. They should be taken into account while designing the photovoltaic cells, nanolasers and optical spintronics devices, where 2D excitons play a significant role.

[Soybean lectin as a component of a composite biopreparation involving Bradyrhizobium japonicum 634b].

The effects of the composite biopreparation Bralec (involving the soybean-specific root nodule bacterium Bradyrhizobium japonicum strain 634b and soybean lectin at concentrations of 500, 50, and 5 microg/ml as major components) on the development and functional activity of soybean-rhizobium symbiosis (development phases of one leaf, four true leaves, and budding) was studied. It was demonstrated that pretreatment of seed with this preparation stimulated the development of both the macro- and microsymbionts. The experimental plants displayed an active accumulation of biomass (by 4-42% higher compared with the variant with inoculation), development of root nodules (the number increased by 11-110% and the weight, by 27-157%). and elevated nitrogen-fixing activity (by 45-204%). The soybean yield increased by 8-10% upon treatment with Bralec 500 and Bralec 5 as compared with the traditional seed bacterization with root nodule bacteria.

[Study of chemotaxis of nodule bacteria of lupin to organic substances].

Ability of different strains (359a, 400, 176, 365a) of nodule bacteria of lupin Bradyrhizobium sp. (Lupinus), which differ in symbiotic properties (competitiveness and nitrogen-fixing activity), to chemotaxis with respect to the organic substances revealed in root exudates of lupin (aminoacids, sugars, organic acids and their salts) has been investigated. It is shown, that alongside with the substances to which rhizobia of lupin, irrespective of their symbiotic properties, show the chemotaxic reactions, there is a number of substances which are specific with respect to different strains of bacteria. Selectivity in chemotaxis of the nodule bacteria depends on their competitiveness. The relations between nitrogen-fixing activity of strains and their ability to chemotaxis are not established.

[The significance of exometabolites in the formation and operation of the soybean-rhizobium symbiosis]. / Rol' ékzometabolitov v protsesse formirovaniia i funktsionirovaniia soevo-rizobial'nogo simbioza.

The effect of various inoculates of the soybean-specific strain of nodule bacteria Bradyrhizobium japonicum 634b (unwashed cells, cells washed from the exopolysaccharide-protein complex, and cells combined with the complex) on the formation and operation of soybean-rhizobium symbiosis. It was shown that addition of the exopolysaccharide-protein complex doubled the ability of the microsymbiont to form nodules, nodule weight, and the nitrogenase activity of the nodules. Bradyrhizobium japonicum 634b cells washed from exometabolites had lower indices of symbiotic activity than their intact counterparts.