Vol 25, No 1 (2022)

The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence o

Abstract – The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system «two qubits + resonator field mode» is obtained. To solve the quantum equation of evolution, the representation of «dressed» states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of «dressed» states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

f Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system «two qubits + resonator field mode» is obtained. To solve the quantum equation of evolution, the representation of «dressed» states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of «dressed» states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

This article is devoted to the derivation of results for the average delay of requests in the queue for a queuing system formed by two flows with the laws of interval distributions in the form of second-order hyperexponential and Erlang distributions shifted to the right. In queuing theory, studies of G/G/1 systems are relevant due to the fact that there is no solution in the final form for the general case. Therefore, in the study of such systems, various particular distribution laws are used as an arbitrary distribution law for G. In this case, the use of the hyperexponential distribution law ensures the coefficient of variation of the input flow intervals is large units, and the Erlang distribution is less than one. To solve the problem posed, the method of spectral decomposition of the solution of the integral Lindley equation was used, which plays an important role in the queueing theory. This method made it possible to obtain a solution for the average delay of requests in the queue for the system under consideration in a closed form. As is known, the remaining characteristics of the queuing system are derived from the average delay of requests.

We describe the iterative algorithm for television image superposition. The superposition is defined by offsets, scale, and rotates. Also additive and multiplicative noise influences the image. The main aim of developing this algorithm is to reduce the time of processing images for estimation superposition parameters. Reducing processing time is provided by reducing the set of reference points, which defines the superposition. The initial coordinate of the reference points is refined at the process of the algorithm work for acceptable superposition of the television images. The superposition parameters are divided into two groups. Offsets belong to the first group, scale and rotate belong to the second group. The parameters in each group are estimated independently. The iterative procedure uses the offsets for estimation scale and rotate, and after it uses scale and rotates for estimation of the offsets. This process is repeated. The next iteration approximates the rate to the real value of the superposition parameters. The developed algorithm allows reducing processing time at 25 times faster than the brute force algorithm for the test data. The test data include two images; the first image has the resolution 288 × 384 pixels, the second image has the resolution 128 × 128 pixels. The second image is the fragment of the first image. Also at the end of the article, the numerical simulation had been presented. The simulation shows the dependences of error estimation of parameters from the noise power.

This article presents the results of modeling a communication system with OFDM using the methods of scrambling the transmitted signals and masking the transmitted information. The paper considers a method of scrambling the transmitted information with pseudo-random sequences obtained by a generator built on the basis of modified dynamic systems. Estimates of the probability of a bit error of the communication system under consideration are obtained, the peak-factor of signals, the correlation characteristics of the scrambled and initial information are estimated, and the entropy of the transmitted information. The results of the article can be used in the design of modern communication systems in order to increase the security of transmitted information and reduce the peak to average power ratio of the generated signals.

Based on the original algorithm for generating three periodic surfaces implemented in the ToposPro information and analytical system, a mathematical model of a porous material was developed. The TPS Extractor software for the computer implementation of this model was developed. This software implements original algorithms for triangulation, translation, smoothing, and model solidifying. The developed triangulation algorithms were used to construct a set of three periodic surfaces, and models of the corresponding porous materials were built on their basis. Based on models of porous materials, a study of the performance of smoothing and translation algorithms was conducted. Using a solidifying algorithm for increasing the model thickness, models of porous material were created that are suitable for 3D printing. Also, samples of porous models were printed out using fused deposition modeling technology.