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We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes adiabatically its sign. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again, but with the proportionality coefficient higher than in the initial state. The concrete value of this proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the adiabatic ratio of the initial ground state (with zero radial and angular quantum numbers) triplicates if the frequency tends to zero linearly as function of time. If the Larmor frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of the time intervals between zero points, so that the mean energy behavior can be quasi-stochastic after many passages through zero value. The original Born-Fock adiabatic theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many instantaneous Fock states, whose weights do not depend on time in the new adiabatic regime., 15 pages, 3 figures

We study the evolution of the energy of a harmonic oscillator when its frequency slowly varies with time and passes through zero value. We consider both the classical and quantum descriptions of the system. We show that after a single frequency passage through zero value, the famous adiabatic invariant ratio of energy to frequency (which does not hold for zero frequency) is reestablished again, but with the proportionality coefficient dependent on the initial state. The dependence on the initial state disappears after averaging over phases of initial states with the same energy (in particular, for the initial vacuum, Fock and thermal quantum states). In this case, the mean proportionality coefficient is always greater than unity. The concrete value of the mean proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the mean energy triplicates if the frequency tends to zero linearly. If the frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on lengths of time intervals between zero points, so that the mean energy behavior turns out quasi-stochastic after many passages through zero value. The original Born-Fock theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many Fock states, whose weights do not depend on time in the new adiabatic regime. When the mean energy triplicates, the initial Nth Fock state becomes a superposition of, roughly speaking, 6N states, distributed non-uniformly. The initial vacuum and low-order Fock states become squeezed, as well as initial thermal states with low values of the mean energy., 17 pages, 9 figures

We study numerically the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying the main attention to their differences from the standard (Klauder--Glauber--Sudarshan) coherent states, especially in the case of high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is, roughly, twice weaker than for the vacuum squeezed states. The Robertson--Schr\"odinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of (non)Gaussianity of CPS are considered., Comment: 14 pages, 8 figures, 88 references

We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the moving center acceleration. In the case of a constant acceleration, the probabilities oscillate with the oscillator frequency, so that no excitation occurs after every period. Examples of oscillating and rotating motion of the harmonic trap center are considered too. Estimations show that the effect of excitation of vibration states due to the motion of the harmonic trap center can be observed in available atomic traps.

The article examines trends in the inflow of foreign investments from countries that are Kazakhstan’s leading partners in this area. Changes in the dynamics of foreign investments incoming flows in terms of their gross and net inflows, the state and changes in their typical and sectoral structure are analyzed. The situation as a whole and in relation to each of six largest investor countries of Kazakhstan is considered. It also examines the inflow of investments from the selected countries into manufacturing industry – a key branch in the context of the modernization of the Kazakhstan economy.

The situation on the foreign exchange market of Kazakhstan over the past few years has been characterized by ambiguous trends and increased devaluation expectations. Problems in the field of exchange rate formation include the adequacy of the level of the tenge exchange rate, its weak predictability, as well as the loss of connection with objective factors that determined the course dynamics over a long period. The increase in uncertainty in the foreign exchange market of Kazakhstan coincided in time with the aggravation of problems in the field of public finance, in particular, with the period of progressive reduction in the volume of the National Fund, as well as the need to ensure the return on pension assets in the face of instability of the national currency. This coincidence suggests that it is the investment activity of the largest state institutions represented by the National Fund, the ENPF and the need to ensure their acceptable profitability in difficult external conditions that have become a new factor that has a serious impact on the currency market of Kazakhstan. This hypothesis is considered in the article, and for the purpose of its assessment, the relationship between the key parameters of the activity of these institutions, their profitability and the tenge exchange rate over the past few years is analyzed.

Here, we present a critical review of recent developments in Casimir physics motivated by discoveries of novel materials. Specifically, topologically nontrivial properties of the graphene family, Chern and topological insulators, and Weyl semimetals have diverse manifestations in the distance dependence, presence of fundamental constants, magnitude, and sign of the Casimir interaction. Limited studies of the role of nonlinear optical properties in the interaction are also reviewed. We show that, since many new materials have greatly enhanced the nonlinear optical response, new efficient pathways for investigation of the characteristic regimes of the Casimir force need to be explored, which are expected to lead to new discoveries. Recent progress in the dynamical Casimir effect is also reviewed and we argue that nonlinear media can open up new directions in this field as well.

We consider a quantum charged particle moving in the $xy$ plane under the action of a uniform perpendicular constant magnetic field, in the presence of a parabolic binding potential. The magnetic-moment operator has a continuous spectrum, and its eigenfunctions in the momentum representation are expressed in terms of modified Bessel functions. The probability distribution of the magnetic moment in the thermodynamic equilibrium state is calculated. At zero temperature, it has a simple exponential form in the diamagnetic region, with a sharp jump to zero at the origin. With an increase of temperature, a paramagnetic wing of the distribution becomes more and more pronounced. In the high-temperature regime, the diamagnetic and paramagnetic wings of the distribution have almost identical forms, described with a high precision by simple exponential functions with very large extensions. Therefore, diamagnetic and paramagnetic contributions almost cancel each other. The remaining non-zero diamagnetic value is due to a small asymmetry of the distribution nearby the origin, where some nonexponential fine structure is observed. The total width of the distribution function strongly depends on the strength of the binding potential. Strong fluctuations of the magnetic moment (described in terms of the variance) are discovered in all temperature regimes.

The measurement of the jet cross sections by the H1 collaboration had been compared to various predictions including the next-to-next-to-leading order (NNLO) QCD calculations which are corrected in this erratum for an implementation error in one of the components of the NNLO calculations. The jet data and the other predictions remain unchanged. Eight figures, one table and conclusions are adapted accordingly, exhibiting even better agreement between the corrected NNLO predictions and the jet data.

We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states), they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters, they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

В статье рассматривается роль государственного сектора в экономике Казахстана от наиболее общих параметров до присутствия предприятий с государственным участием на уровне макроотраслей. Казахстан отличается высокой ролью в экономике государственных и квазигосударственных компаний, поэтому основной акцент в анализе сделан на роли государственного предпринимательства. Проведен анализ абсолютных и относительных параметров роли государственных предприятий в экономике и основных видах деятельности, рассмотрена их динамика, проведена оценка влияния государственного предпринимательства на рост ВВП и производства в основных сферах экономики.

The European physical journal / C 81(8), 738 (2021). doi:10.1140/epjc/s10052-021-09394-0, Published by Springer, Heidelberg

We consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, and orthogonal even coherent states (or compass states). The new element is the analysis of products of the corresponding (co)variances and the related generalized (Robertson&ndash, Schr&ouml, dinger) intelligent states (RSIS). In particular, we show that both Fock and pure Gaussian homogeneous states are RSIS for the fourth powers (but not for the sixth ones). We show that lower bounds of the high-order uncertainty products can be significantly below the vacuum values. In this connection, the concept of significant and weak high-order squeezing is introduced.

This is a digest of the main achievements in the wide area, called the Dynamical Casimir Effect nowadays, for the past 50 years, with the emphasis on results obtained after 2010.

In recent decades, the prevalence of hyperuricemia (HU) is increasing worldwide; the role of uric acid (UA) in the genesis of various metabolic disorders, cardiovascular diseases, and kidney disease is being discussed. There are very few investigations of the rate of HU and its role in the development of diseases in certain social groups, including in professional athletes.Objective:to estimate the prevalence of HU and its role in the genesis of various pathological conditions and metabolic disturbances in professional athletes.Patients and methods.A retrospective comparative one-stage study was conducted, for which 2148 athletes who met inclusion criteria were selected and examined in the Federal Research and Clinical Center for Sports Medicine and Rehabilitation, Federal Biomedical Agency, in 2015. A control group consisted of 99 ageand sex-matched healthy volunteers examined at the V.A. Nasonova Research Institute of Rheumatology in 2017. The analysis included a comparison of the rate of HU and other examined parameters in professional athletes and healthy volunteers. The examined parameters were separately compared in athletes with/without HU, followed by statistical processing of results.Results.HU was detected in 306 (14.2%) of the 2148 athletes, more often in men (n=253 (20%) than in women (n=53 (6%); (pConclusion.HU is detected quite often in professional athletes (14.2%), which is comparable with the indicators seen in healthy volunteers (12.1%). The high prevalence of HU and its association with indicators reflecting kidney function, lipid metabolic disturbances, and BMI necessitate further investigations aimed at searching the causes of HU and methods of its prevention and treatment in professional athletes.

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [−y(1 + β), x(1 − β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.

We consider a quantum spinless nonrelativistic charged particle moving in the $xy$ plane under the action of a time-dependent magnetic field, described by means of the linear vector potential ${\bf A}=B(t)\PG{-y(1+\alpha),x(1-\alpha)}/2$, with two fixed values of the gauge parameter $\alpha$: $\alpha=0$ (the circular gauge) and $\alpha =1$ (the Landau gauge). Although the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for $\alpha=0$ and straight lines for $\alpha=1$. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function $B(t)$. They are expressed in terms of solutions to the classical equation of motion $\ddot\vep +\omega_{\alpha}^2(t) \vep=0$, with $\omega_1=2\omega_0$. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions $B(t)$, when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case, as well. The case of slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value., Comment: 50 pages, 24 figures. The title and text are expanded. This version is close to the published paper (except for formatting)

The motion of an artificial Earth satellite with constant absolute value of the acceleration is considered. This requirement is equivalent to imposing a second-order nonlinear nonholonomic constraint or a third-order linear nonholonomic constraint. Two theories of motion of nonholonomic systems with high-order constraints are used for solving this problem. According to the first theory, a consistent system of differential equations is constructed with respect to the generalized coordinates and the Lagrange multipliers; the second theory is based on the application of the generalized Gauss principle. The results are different, although the constraints are satisfied in both theories. It turns out that infinitely many solutions can be built, but using these theories one can find two specific solutions. The question of the difference of these two solutions from the set of all other possible solutions is raised. We also simplify the previously obtained differential equations. The transition to dimensionless variables is made. Three parameters of motion prior to imposition of the constraint are single out, which control the motion after the application of the constraint. The solutions obtained from these theories of motion of nonholonomic systems are compared.

The paper is based on the talk with the same name given at the International scientific conference on mechanics “The Ninth Polyakhov’s Reading” dedicated to the 200th anniversary of the birth of the prominent Russian scientist Pafnuty Lvovich Chebyshev. The generalized Chebyshev problem is formulated, in which the motion of a system in the presence of given generalized forces should satisfy an additional system of linear differential equations in which the order of each equation exceeds three. These problems constitute a new class of control problems in which the motion program is given in the form of the above additional system of differential equations. These equations can be considered as linear nonholonomic constraints of high order, whose reactions are the desired control forces. To solve such problems, two theories were developed at the Department of Theoretical and Applied Mechanics of St. Petersburg University. In the first theory, we construct a consistent system of differential equations for the generalized coordinates and the Lagrange multipliers, which are considered as equitable unknown functions of time. The second theory is based on the generalized Gauss principle. The application of the theory is illustrated by the solution of a real space mechanics problem about the motion of an Earth satellite after fixing the value of its acceleration at some point in time. Especially efficient is the application of the second theory to the determination of the optimal control force for transferring a mechanical system with a finite number of degrees of freedom from an existing phase state to a new specified state within a specified period of time. The new method is used to solve the model problem of controlled horizontal motion of a cart bearing the axes of several mathematical pendulums. It is shown that the use of the generalized Gauss principle for solving this problem is undoubtedly superior to that of the classical Pontryagin maximum principle.

We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the most general linear vector potential of the form A = B ( t ) − y ( 1 + α ) , x ( 1 − α ) ∕ 2 . Such potentials with α ≠ 0 can be created inside infinite solenoids with non-circular cross sections. The physical properties, such as energy and magnetic moment, do not depend on the choice of gauge in the thermodynamic equilibrium state. But systems with different values of α are not equivalent for nonstationary magnetic fields, due to different structures of induced electric fields. Using the approximation of the stepwise variation of the magnetic field, we obtain explicit formulas describing the change of the energy and magnetic moment from the initial equilibrium state, created with the aid of a weak anisotropic harmonic potential. The results are quite different for different values of the gauge parameter α , as well as for the initial high temperature and low temperature states. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields. In addition, the magnetic moment becomes a strongly oscillating function of time after the jump of the field. Strong fluctuations of the magnetic moment (described in terms of the variance) are discovered in all regimes, including the initial equilibrium state. These fluctuations are sensitive to the shape of the trap confining the particle initially. Moreover, these fluctuations do not depend on the Planck constant in the high temperature case, and the magnetic moment variance is much bigger than the square of mean magnetic moment.

We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) &minus, y ( 1 + &beta, ) , x ( 1 &minus, &beta, ) / 2 . Such potentials with &beta, &ne, 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of &beta, are not equivalent for nonstationary magnetic fields or time-dependent parameters &beta, ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields.

The scenario of a single-mode cavity with harmonically modulated frequency is revisited in the presence of strongly detuned qubit or cyclic qutrit. It is found that when the qubit frequency is close to $3\nu $ there is a peak in the photon generation rate via four-photon transitions for the modulation frequency $4\nu $, where $\nu $ is the average cavity frequency. Effective five-photon processes can occur for the modulation frequency $5\nu $ in the presence of a cyclic qutrit, and the corresponding transition rates exhibit series of peaks. Closed analytical description is derived for the unitary evolution, and numeric simulations indicate the feasibility of multi-photon dynamical Casimir effect under weak dissipation., Comment: 10 pages, 5 figures

We study a circuit QED setup involving a single cavity mode and a cyclic qutrit whose parameters are time modulated externally. It is shown that in the dispersive regime this system behaves as a versatile platform to implement effective $n$-photon Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) models by suitably setting the modulation frequency. The atomic levels and the cavity Fock states involved in the effective Hamiltonians can be controlled through adjustment of the system parameters, and different JC and AJC interactions can be implemented simultaneously using multitone modulations. Moreover, one can implement some models that go beyond simple JC and AJC-like interaction, such as multiphoton coupling between certain entangled states. We estimate analytically the associated transition rates and study numerically the dynamics in the presence of Markovian dissipation, demonstrating that lower-order effective Hamiltonians can be implemented with current technology.

The problem of finding covariance matrices that remain constant in time for arbitrary multi-dimensional quadratic Hamiltonians (including those with time-dependent coefficients) is considered. General solutions are obtained.

Analytical solutions to the problem of mode splitting caused by a thin plain magnetized slab placed in a rectangular electromagnetic cavity are found in two special cases: an infinite slab between two ideal infinite plain mirrors (1D model) and a 2D model of a cavity confined in the direction of permanent magnetization. Under the resonance conditions, the time-dependent magnetization vectors inside the slab are strongly enhanced, with opposite directions in the split modes. For realistic parameters, the frequency splitting does not depend on the dielectric constant of the slab and the Landau-Lifshitz-Gilbert damping coefficient, whereas the loaded cavity quality factor is not sensitive to the slab position.

We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for the time-dependent Wigner function are obtained. The time of disappearance of the so called “sub-Planck structures” is calculated using the negative value of the Wigner function at the origin of phase space. It is shown that this value rapidly decreases during a short “conventional interference degradation time” (CIDT), which is inversely proportional to the size of quantum superposition, provided the anti-Hermitian terms in the master equation are of the same order (or stronger) as the Hermitian ones (governing the parametric amplification). The CIDT is compared with the final positivization time (FPT), when the Wigner function becomes positive. It appears that the FPT does not depend on the size of superpositions, moreover, it can be much bigger in the amplifying media than in the attenuating ones. Paradoxically, strengthening the Hamiltonian part results in decreasing the CIDT, so that the CIDT almost does not depend on the size of superpositions in the asymptotical case of very weak reservoir coupling. We also analyze the evolution of the Mandel factor, showing that for some sets of parameters this factor remains significantly negative, even when the Wigner function becomes positive.

Excitation of volume and surface magnetostatic spin waves in ferrite garnet films by circularly polarized laser pulses utilizing to the inverse magnetooptical Faraday effect has been studied experimentally. The region of excitation of the magnetostatic spin waves is determined by the diameter of the laser beam (∼10 μm). At the same time, the characteristic propagation length of the modes is 30 μm. A method of finding the local characteristics of a magnetic film, in particular, the cubic and uniaxial anisotropy constants, based on the analysis of the azimuthal-angle dependence of the spectrum of the magnetostatic spin waves has been proposed.

We consider the interaction between a single cavity mode and N ≫ 1 identical qubits, assuming that any system parameter can be rapidly modulated in situ by external bias. It is shown that, for the qubits initially in the ground states, three photons can be coherently annihilated in the dispersive regime for harmonic modulation with frequency 3 ω 0 − Ω 0 , where ω 0 ( Ω 0 ) is the bare cavity (qubit) frequency. This phenomenon can be called “Anti-dynamical Casimir effect”, since a pair of excitations is destroyed without dissipation due to the external modulation. For the initial vacuum cavity state, three qubit excitations can also be annihilated for the modulation frequency 3 Ω 0 − ω 0 .

We revisit the dynamical Casimir effect in high-quality multimode cavities, namely, generation of photons from vacuum due to fast external variation of system parameters. In one-dimensional case the spectrum of modes is equidistant, so for harmonic modulation an infinite number of modes become excited. But only one mode is usually excited in cavities with nonequidistant spectrum, apart from some exceptional configurations for which two or three modes are populated. Here is unveiled another scenario in which a small number of photons is generated from vacuum in two specific modes of a cavity with special spectrum profile. The scheme relies on strongly coupling the field to an initially unexcited qubit, whose frequency undergoes a weak harmonic perturbation. When the ratio between two modes' frequencies is accurately tuned in the vicinity of 3, these modes and the qubit can be driven to tripartite entangled states due to narrow three-photon resonances.

Dynamical Casimir effect (DCE) denotes a plethora of phenomena characterized by generation of quanta (usually photons) from vacuum due to modulation of parameters of some neutral system. Its counterpart, or Anti-DCE, can be defined as a process in which photons, as well as overall system excitations, are annihilated from the thermal state of the field due to variation of system parameters. In this paper is proposed a new fast scheme for Anti-DCE based on coupling a single-mode cavity to a qubit with time-dependent coupling strength g = e sin ⁡ η t , where the modulation frequency η is a linear or quadratic function of time and e lies in the ultrastrong coupling regime. Numeric solutions of time-dependent Rabi Hamiltonian illustrate some convenient forms of η that reduce the average number of system excitations for initial thermal and Poissonian mixed states, and modification of the photon statistics is discussed.

We consider the relaxation of the quantum harmonic oscillator in the framework of the standard master equation. Analyzing the known solutions, we have found some new interesting effects. Namely, we show that the evolution of some parameters, such as the energy fluctuations, the Mandel factor, the invariant uncertainty product and quantum purity, can exhibit non-monotonous behavior with big deviations from the initial and final values. Also, we show that highly excited initial Fock states maintain their non-classical nature longer than low excited ones. During the evolution, the quantum purity of these states stays at almost constant low level during a long period, after the fast decrease initially and before the fast return to the final value at the end.

Agricultural production is a specific branch of economic activity, which is basic in the economy of the region and has a number of significant features that affect the efficiency of production sales. The objective of the study is to examine the prospects of using blockchain technology in the field of agriculture and development of rural territories, based on the analysis of scientific publications, as well as domestic and foreign cases.At the moment, the experience of using blockchain technology in agriculture is insignificant. The blockchain-based agricultural system can simplify every stage of creation and distribution of products. The use of blockchain technology is quite practical in specific sectors of agricultural activity. They are described in step-by-step instructions for using blockchain technology for farmers created by the Emercoin team. The main advantages of blockchain technology for the agricultural sector are the following: exchange of products without the mediation of a third party; safety and reliability of transactions; high quality data; work with qualified users; process integrity; transparency and permanence of the system; simplified accounting system; efficient transactions. The potential for the use of blockchain technology in the agricultural sector is very high and will enhance the development of not only agricultural producers themselves, but also rural areas.

This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided.