Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

We theoretically study a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also re-examine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential, as well as excitation energies for broken-axisymmetry state. We show that the broken-axisymmetry state can be prepared at three different regimes of applied magnetic field. We also present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.Comment: 14 pages, 2 figures, 4 table

Zero sound in a quantum gas of spin-3/2 atoms with multipole exchange interaction

In the context of quantum gases, we obtain a many-body Hamiltonian for spin-3/2 atoms with general multipole (spin, quadrupole, and octupole) exchange interaction by employing the apparatus of irreducible spherical tensor operators. This Hamiltonian implies the finite-range interaction, whereas, for zero-range (contact) potentials parameterized by the $s$-wave scattering length, the multipole exchange interaction becomes irrelevant. Following the reduced description method for quantum systems, we derive the quantum kinetic equation for spin-3/2 atoms in a magnetic field and apply it to examine the high-frequency oscillations known as zero sound.Comment: 21 pages, 2 figure

Second quantization method in the presence of bound states of particles

We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of compound particles). In this approximation the compound and elementary particles are considered on an equal basis. This means that creation and annihilation operators of compound particles can be introduced. The Hamiltonians, which specify the interactions between compound and elementary particles and between compound particles themselves are found in terms of the interaction amplitudes for elementary particles. The nonrelativistic quantum electrodynamics is developed for systems containing both elementary and compound particles. Some applications of this theory are considered.Comment: 35 page

CROP YIELD AND QUALITY OF PEARS GROWN ON OPTIMIZING THE SOIL NUTRITION AND WITH DIFFERENT FOLIAR FEEDING

This work presents the results of the research conducted within 2015 field experiment, which was done according to a two-factor scheme replicated three times. The experiment involved eight сontrol trees on each elementary plot. Before the experiment was carried out, by agrochemical soil analyzing of the potassium mobile forms content, it had been found to be by 46 mg / kg fewer than the average value of the optimal level, and nitrate nitrogen (by the soil nitrification ability) and mobile phosphorus compounds - more than the optimal levels ofthose. To optimize the soil background, a K2O rate of 598 kg / ha was calculated and applied, and, thus, an optimized background for the pear soil mineral nutrition with all three major macronutrients (NPK) was created. The scheme of the study includes two levels of compounds and forms of nitrogen (N), phosphorus (P2O5) and potassium (K2O) available insoil: non-optimized (with no soil fertilizing) and optimized - bymeans of agrochemical soil fertilizers with the macronutrients which lack in the soil root zone (0-60 cm) inreaching the optimal levels (factor A), and four variants of foliar feeding: 1 – with no additional fertilizing (spraying leaf cover with water), 2, 3 and 4 – spraying with fertilizerpreparations solutions respectively, as follows: Reakom plus (garden-vegetable garden) – 5 l/ha, Vuksal Microplant – 3 l/ha and Biohelat "Fruit-berry crop" – 3 l/ha (factor B). The stated doses of the preparations were dissolved at the ratio of 1000 l of solution per 1 hectare of the garden. Sufficient levels of nitrogen and phosphorus compounds(which much exceed the optimal levelsof those for apple trees) available in ordinary chernozem for plants, and insufficient potassium supply (less than the optimal level of its exchange forms per 46 mg / kg of soil) сaused a sufficient K2O 598 kg / ha feeding for the pear trees with thisnutrient and the general optimized background for their mineral nutrition with the main macronutrients (NPK), which was maintained during the three-year study period. With an optimized background of soil nutrition, the highest productivity of the Tavriiska pear variety was provided by the four-time foliar feeding of trees by means of fertilizer preparation Vuksal Microplant; the crop yield was 33.5% higher as compared with its level (17.6 t / ha) with an non-optimized background. The increase in crop yield was due to a more abundant trees flowering (by 30.2– 34.9%), greater fruit inception(by 3.0– 3.5%) and keeping of fruits in the trees before harvesting by 16.3– 20.7%, and also due toan increase in their average weight by 9.9 – 11.0%. Optimizing the soil mineral nutrition of the pear and foliar feeding has resulted inan increase in fruit marketability – the yield of the superior and the first fruit commercial grades is relatively higher by 5.7 – 6.5%