Classical approach in quantum physics

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom recently discovered with the help of Poincar$\acute{\mathrm{e}}$ section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treating as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well. In conclusion, the relation between quantum theory, classical physics and measurement is discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment "The author has made many worthwhile contributions to semiclassical physics, but this article does not meet the standard for a topical review"

The hydrogen atom in electric and magnetic fields : Pauli's 1926 article

The results obtained by Pauli, in his 1926 article on the hydrogen atom, made essential use of the dynamical so(4) symmetry of the bound states. Pauli used this symmetry to compute the perturbed energy levels of an hydrogen atom in a uniform electric field (Stark effect) and in uniform electric and magnetic fields. Although the experimental check of the single Stark effect on the hydrogen atom has been studied experimentally, Pauli's results in mixed fields have been studied only for Rydberg states of rubidium atoms in crossedfields and lithium atoms in parallel fields.Comment: 11 pages, latex file, 2 figure

General solution of equations of motion for a classical particle in 9-dimensional Finslerian space

A Lagrangian description of a classical particle in a 9-dimensional flat Finslerian space with a cubic metric function is constructed. The general solution of equations of motion for such a particle is obtained. The Galilean law of inertia for the Finslerian space is confirmed.Comment: 10 pages, LaTeX-2e, no figures; added 2 reference

On foundations of quantum physics

Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between 'canonically conjugated' coordinate and momentum operators leads to a wrong version of quantum mechanics. The origin of time is analyzed in detail by the example of atomic collision theory. It is shown that for a closed system like the three-body (two nuclei + electron) time-dependent Schroedinger equation has no physical meaning since in the high impact energy limit it transforms into an equation with two independent time-like variables; the time appears in the stationary Schroedinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system. Following the Einstein-Rozen-Podolsky experiment and Bell's inequality the wave function is interpreted as an actual field of information in the elementary form. The relation between physics and mathematics is also discussed.Comment: This article is extended version of paper: Solov'ev, E.A.: Phys.At.Nuc. v. 72, 853 (2009

Eigenvibrations of a beam with load

© 2017, Pleiades Publishing, Ltd. The eigenvalue problem describing eigenvibrations of a beam with load is investigated. The problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. Limit properties of eigenvalues and eigenfunctions are studied

Theoretical and numerical studies of wave-packet propagation in tokamak plasmas

Theoretical and numerical studies of wave-packet propagation are presented to analyze the time varying 2D mode structures of electrostatic fluctuations in tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave equations directly, the solution of the initial value problem is used to obtain the 2D mode structure, following the propagation of wave-packets generated by a source and reconstructing the time varying field. As application, the 2D WKB method is applied to investigate the shaping effects (elongation and triangularity) of tokamak geometry on the lower hybrid wave propagation and absorbtion. Meanwhile, the Mode Structure Decomposition (MSD) method is used to handle the boundary conditions and simplify the 2D problem to two nested 1D problems. The MSD method is related to that discussed earlier by Zonca and Chen [Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40, 396 (1978)], when spatial scale separation applies. This method is used to investigate the time varying 2D electrostatic ITG mode structure with a mixed WKB-full-wave technique. The time varying field pattern is reconstructed and the time asymptotic structure of the wave-packet propagation gives the 2D eigenmode and the corresponding eigenvalue. As a general approach to investigate 2D mode structures in tokamak plasmas, our method also applies for electromagnetic waves with general source/sink terms, either by an internal/external antenna or nonlinear wave interaction with zonal structures.Comment: 24 pages, 14 figure

ИССЛЕДОВАНИЕ МЕТОДОВ ОПРЕДЕЛЕНИЯ ВРЕМЕННЫХ НОРМАТИВОВ ЗАМЕНЫ КРЕПЕЖНЫХ ЭЛЕМЕНТОВ АВИАЦИОННОЙ ТЕХНИКИ

The study of the methods revealed their advantages and disadvantages for further synthesis and optimization. The main task was to improve the most suitable method, which will have the maximum number of affecting factors. The experimental method is highly accurate, but it requires high costs to work on analogues for each specific type of fasteners. The calculated method based on a single experiment allows to determine time standards for various fasteners. The given method does not require high costs for experiments, but like the experimental method, does not take into account performance degradation with continuous operation time. This leads to serious errors in obtaining time standards for a large number of fasteners. The article shows the optimized model of calculated method, based on a linear approximation of dependence of the number of fasteners replacements (removals/installations) on time at multiple intervals. The optimized model allows to obtain time standards of typical fasteners replacement with different geometric characteristic taking into account performance degradation over time. Several experiments on the aircraft were conducted for testing the improved calculated method. On the basis of the experimental data the researchers built graphs of the number of fasteners replacements (removal/installation) on time with different geometric characteristics taking into account performance degradation over time. The data obtained is advisable to use for calculation maintainability factors on aircraft design stages. Program realization of these methods and systematization of the received time standards allow to improve maintainability, due optimization number and position of airframe fasteners and systems units and aviation equipment for the aircraft being designed and modernized. Application of the automated systems of design and analysis will contribute to labor input decrease at the aircraft maintainability analysis.Исследование методов получения временных нормативов работы с крепежными элементами позволило выявить их недостатки и преимущества для дальнейшего синтеза и оптимизации. Основной задачей являлось улучшение наиболее подходящего метода для учета максимального количества влияющих факторов. Экспериментальный метод имеет высокую точность, но требует высоких затрат на проведение работ на объектах-аналогах для каждого конкретного типа крепежного элемента. Расчетный метод, основанный на получении нормативов времени для различных крепежных элементов, по данным одного эксперимента, не требует больших затрат на получение нормативов времени. Однако так же, как и экспериментальный метод, расчетный метод не учитывает снижение производительности со временем непрерывной работы. Этот недостаток ведет к существенным погрешностям при получении нормативов для большого количества крепежных элементов. В работе показана оптимизированная модель расчетного метода, которая основывается на линейной аппроксимации интервалов графика зависимости числа снятых/установленных крепежных элементов от времени работы. Оптимизированная модель позволяет получить временные нормативы для типовых крепежных элементов с различными геометрическими характеристиками и учетом снижения производительности со временем. Для апробации улучшенного расчетного метода был проведен ряд экспериментов по замеру времени работы с крепежными элементами во время регламентных работ летательного аппарата. В результате были построены графики зависимости работы с однотипными крепежными элементами с учетом снижения производительности труда, которые целесообразно использовать как справочные данные для расчета показателей эксплуатационной технологичности на этапах разработки авиационной техники. Программная реализация данных методов и систематизация полученных временных нормативов позволяет улучшить ЭТХ за счет оптимизации количества и расположения крепежных элементов планера, агрегатов систем и оборудования разрабатываемого или модернизируемого летательного аппарата. Применение систем автоматизированного проектирования и анализа будет способствовать снижению трудоемкости при анализе эксплуатационной технологичности конструкций летательных аппаратов

ПРОБЛЕМЫ ОЦЕНКИ ЭФФЕКТИВНОСТИ ИНДИВИДУАЛЬНО-НАКОПИТЕЛЬНОЙ МОДЕЛИ ПЕНСИОННОГО СТРАХОВАНИЯ

Topic. The article presents the results of actuarial analysis of the newest and most controversial component of the Russian system of compulsory pension insurance — accrual one. The prospect of its further development is estimated. The effectiveness of this method of pension provision is assessed by the author from the point of view the role and degree of performance of the institutional functions of the state pension system (i.e., ensuring a decent level of material security of pensioners), and the possibility of achieving the targets formulated in 2012 in the government’s Strategy for the long-term development of the pension system of the Russian Federation.Purpose. Development of economically reasoned justification of real financial relations between participants of the insurance pension system within the framework of individual-accrual models of pension provision.Methodology. The main methodological feature and originality of this study is a multi-factor analysis, using methods of comparative analysis and actuarial forecasting of the whole set of conditions for the formation and implementation by insured persons of their pension rights in the individual-accrual model (both external to the pension system and internal as well), not carried out in other studies on this problem.Results.The article presents the results of economicstudies of the national practice of formation and implementation of pension rights of workers in the framework of the individual-accrual pension insurance program. Those results can be used in substantiating the directions of reforming the accrual methods of pension provision:The degree of direct dependence of the pension system efficiency on external macroeconomic and demographic factors is proved.We formulated criteria for evaluating the effectiveness of the accrual component of the pension system.It is given the characteristic and the main tasks of the accrual component of the compulsory pension insurance system.There are proposed measures to improve the functioning of the accrual component in the existing Russian reality and in the long term.Conclusions. The accrual method of formation and realization of pension rights in specific long-term socioeconomic conditions does not allow the main categories of insured persons to form the level of pensions provided in the solidarity system, and also sharply increases the budgetary risks not only of the Russian Pension Fund (PFR), but also of the Federal budget.В статье представлены результаты актуарного анализа состояния самого нового и наиболее спорного компонента российской системы обязательного пенсионного страхования — накопительного. Оценивается перспектива его дальнейшего развития. Эффективность данного способа пенсионного обеспечения оценивается автором по роли и степени выполнения институциональных функций государственной пенсионной системы (обеспечения достойного уровня материального благосостояния пенсионеров) и достижения ориентиров, заданных правительственной Стратегией долгосрочного развития пенсионной системы Российской Федерации2012 г.Цель статьи — выработка экономически аргументированного обоснования реальных финансовых отношений между участниками страховой пенсионной системы в рамках индивидуально-накопительных моделей пенсионного обеспечения.Главной методологической особенностью и оригинальностью данного исследования является многофакторный анализ с использованием методов сравнительного анализа и актуарного прогнозирования, всего комплекса условий формирования и реализации застрахованными лицами своих пенсионных прав в индивидуально-накопительной модели (как внешних по отношению к пенсионной системе, так и внутрисистемных), не проводившийся в других исследованиях, посвященных данной проблеме.В статье представлены результаты профессионально-экономических исследований отечественной практики формирования и реализации пенсионных прав работников в рамках индивидуально-накопительной программы пенсионного страхования, которые могут быть использованы при обосновании направлений реформирования накопительных способов пенсионного обеспечения:доказана степень непосредственной зависимости эффективности пенсионной системы от внешних макроэкономических и демографических факторов;выработаны критерии оценки эффективности накопительного компонента пенсионной системы;дана характеристика и сформулированы основные задачи накопительного компонента системы обязательного пенсионного страхования;предложены меры по совершенствованию порядка функционирования накопительного компонента в существующих российских реалиях и в долгосрочной перспективе.В результате исследования сделан вывод о том, что накопительный способ формирования и реализации пенсионных прав в конкретных долгосрочных социально-экономических условиях не позволяет основным категориям застрахованных лиц сформировать уровень пенсий, обеспечиваемый в солидарной системе, а также он резко увеличивает бюджетные риски не только ПФР, но и федерального бюджета

Non-sequential double ionization below laser-intensity threshold: Anticorrelation of electrons without excitation of parent ion

Two-electron correlated spectra of non-sequential double ionization below laser-intensity threshold are known to exhibit back-to-back scattering of the electrons, viz., the anticorrelation of the electrons. Currently, the widely accepted interpretation of the anticorrelation is recollision-induced excitation of the ion plus subsequent field ionization of the second electron. We argue that another mechanism, namely simultaneous electron emission, when the time of return of the rescattered electron is equal to the time of liberation of the bounded electron (the ion has no time for excitation), can also explain the anticorrelation of the electrons in the deep below laser-intensity threshold regime. Our conclusion is based on the results of the numerical solution of the time-dependent Schr\"{o}dinger equation for a model system of two one-dimensional electrons as well as an adiabatic analytic model that allows for a closed-form solution.Comment: 6 pages and 3 figure

Predictive cartography of metal binders using generative topographic mapping

© 2017, Springer International Publishing AG. Generative topographic mapping (GTM) approach is used to visualize the chemical space of organic molecules (L) with respect to binding a wide range of 41 different metal cations (M) and also to b uild predictive models for stability constants (logK) of 1:1 (M:L) complexes using “density maps,” “activity landscapes,” and “selectivity landscapes” techniques. A two-dimensional map describing the entire set of 2962 metal binders reveals the selectivity and promiscuity zones with respect to individual metals or groups of metals with similar chemical properties (lanthanides, transition metals, etc). The GTM-based global (for entire set) and local (for selected subsets) models demonstrate a good predictive performance in the cross-validation procedure. It is also shown that the data likelihood could be used as a definition of the applicability domain of GTM-based models. Thus, the GTM approach represents an efficient tool for the predictive cartography of metal binders, which can both visualize their chemical space and predict the affinity profile of metals for new ligands