Physics of Wave Processes and Radio Systems

Background. To operate a quantum computer, a set of universal gates must be implemented, such as a two-cubit gate of the controlled negation type plus one-cubit spins. As a universal alternative, three-cubic-bit gates may be used. In this regard, it seems very relevant to investigate the dynamics of three-qubit systems in microwave resonators, in particular to study the most efficient schemes for generating, controlling, and monitoring entangled qubit states. Aim. To investigate the features of the dynamics of entangled pairs of qubits for a system in which two qubits are locked in a single-mode resonator and interact with the thermal field mode, and the third qubit is in a free state. Methods. To analyze the dynamics of the considered system, the solution of the quantum Liouville equation for the full density matrix is investigated. The exact solution of the above equation in the case of initial biseparable states of the qubits is found. The exact solution of the evolution equation is used to calculate the criterion of entanglement of qubit pairs – negativity. Numerical simulations of negativity for biseparable qubit states as well as different values of the thermal field intensity of the resonator have been carried out. Results. It is shown that for intense thermal fields of the resonator the effect of instantaneous death of entanglement is observed, while the time intervals between death and revival of entanglement of qubits depend essentially on the choice of their initial biseparable state. It is found that for one of the biseparable states, entanglement of qubits trapped in the resonator does not occur at any field intensities of the resonator. Conclusion. It is found that the peculiarities of the dynamics of entanglement of qubits, in particular the time intervals between the death and birth of entangled qubits, are determined by the choice of the initial biseparable state of qubits, as well as by the values of the field intensity of the resonator. The results obtained can be used to effectively control and manage the degree of qubit entanglement in three-qubit systems in microwave resonators.

Background. In the article, the concept of external barycentric coordinates is introduced to generalize the applicability of the barycentric method in solving external boundary value and initial boundary value problems of mathematical physics. Aim of the work is to form a simple analytical relation that allows calculating barycentric coordinates external to a given arbitrary polygonal area with a given accuracy. Methods. The corresponding ratio is formed when drawing up an approximate analytical calculation rule, which is based on the solution by the Fredholm method of the external Dirichlet problem for the Laplace equation. The basis of this solution is the decomposition of the kernel of the Fredholm integral equation of the second kind by Legendre polynomials of the first and second kind, formed using the Heine formula. Results. The convergence rate of the obtained approximate analytical calculation of the external barycentric coordinates is estimated when establishing exponential convergence in Hilbert space and polynomial convergence in the space of continuous functions. The algorithmic features of the implementation of an approximate analytical solution with a structured representation of pseudocodes of programs for calculating external barycentric coordinates, formed mainly for the MathCad computer algebra system, are clarified. The efficiency is demonstrated by specific examples. Conclusion. The author of the article hopes that the detailed results of the algorithmic implementation of the calculation of external barycentric coordinates will arouse interest and make the publication material more accessible to a wide range of readers, which will lead to the development of the barycentric method in solving boundary and initial boundary value problems of mathematical physics.

Background. In the process of functioning of modern complexes and specialized equipment in conditions of direct visibility between radio facilities, data transmission is not always possible, which significantly reduces the efficiency of the data transmission system and increases the time to search for new locations for transceivers. The reason for this problem may lie in the peculiarities of the terrain, which has an interference and diffraction effect on the propagation of the radio signal. At the same time, analysis and a digital terrain model from earth remote sensing data and the implementation of automated calculations based on it to find the best coordinates in terms of electromagnetic compatibility in the required areas may be of significant interest for solving this problem. Aim. The main purpose of the work is determined by the need to develop algorithms and software implementation of the tool, which will eventually allow, given the characteristics of the hardware, to promptly and adequately analyze the possibility and evaluate the parameters for organizing stable radio communications even at the planning stage using interactive satellite maps. Methods. The article presents the developed algorithms and screenshots of the implementation of the program for calculating the interference effect of the relief, taking into account the underlying surface in the radio communication interval. Results. The results of the program implementation are presented, which calculate the essential propagation zone of the radio signal in accordance with the radio frequency, classifies the channel depending on the presence of terrain obstacles in the essential zone, determines the reflection point on the radio path according to the principle of equality of angles of incidence and reflection and verifies its belonging to the directions of antenna diagrams, takes into account the reflection coefficient at the underlying surface of a water body at the reflection point and calculates the amount of interference losses. Conclusion. A program has been developed that allows you to determine the intensity of the emitter field at any point of the terrain, taking into account obstacles.

Background. Development of radar complex for detection of air, sea, and ground objects, as well as determination of their distance, speed and geometric parameters with automated processing. Aim. Creation of an airborne side-scan radar complex with synthetic aperture mounted on an unmanned aerial vehicle. Methods. Application of digital signal processing methods for formation of radio holograms and extraction of information about objects. Use of algorithms for automatic processing and analysis of the obtained data in real time. Results. The structural-functional scheme of the X-band side-scan radar system consisting of an antenna, a receiving and transmitting unit, a container with a digital core and a micronavigation system is described. In high-resolution mode, a radar hologram formed on board and dropped via a communication channel to the control and processing station. Radar image formation and secondary processing is performed at the ground station in automatic mode. Conclusion. According to the results of the research it is shown that it is possible to realise real-time radar reception on board the carrier, as well as to install the considered airborne side-scan radar complex on an unmanned aerial vehicle together with an automated point of information processing and analysis.

Background. Currently, in geocryology, to predict seasonal changes in the state of frozen rocks and soils, Fourier formulas obtained earlier are widely used, modeling temperature fluctuations in the surface layer of the earth’s crust caused by annual fluctuations in its surface temperature. A significant drawback of this approach to modeling is manifested in the fact that in reality the state of the medium is characterized not only by the temperature field, but also by the moisture content field, which Fourier theory does not contain. Aim. It is required to generalize the Fourier problem known in mathematical physics on fluctuations of the temperature field in half-space by introducing into consideration, along with the temperature field, the moisture content field and taking into account the phenomena of evaporation and condensation associated with this field. Methods. Within the framework of A.V. Lykov’s theory, a spatially one-dimensional mathematical model of the processes of heat and moisture propagation in a homogeneous half-space, the boundary of which is in a state of heat and mass exchange with an airless medium, has been developed. By the method of complex amplitudes, formulas are obtained for time-asymptotic fluctuations in temperature and moisture content in a material filling a half-space, provided that the air temperature changes according to a harmonic law, and water vapor, both near the surface of the material and outside the boundary layer, is in a state close to saturation. Results. According to the results obtained, the temperature field is represented by a superposition of two damped harmonic waves, which have the same frequency, but different attenuation coefficients and phase velocities. The moisture retention field has the same structure. For a material with clay characteristics and with specific values of all the process-defining quantities for each of the waves, the depth of penetration and the delay time of vibrations at a given depth relative to fluctuations in air temperature are calculated, and the results obtained are compared with experimental data. Conclusion. The proposed solution and the following conclusions from it are the development of Fourier studies known in the literature on fluctuations in the temperature field in the surface layer of the Earth’s crust and are valid only in a situation when the material does not contain moisture, and according to the harmonic law, the temperature of the surface of the material does not change. The results of the work can be used in geocryology as a theoretical tool for modeling seasonal fluctuations in the thermal state of frozen rocks and soils.