Canonical quantization of so-called non-Lagrangian systems

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. It turns out that in the general case the hamiltonization and canonical quantization of such an action are non-trivial problems, since the theory involves time-dependent constraints. We adopt the general approach of hamiltonization and canonical quantization for such theories (Gitman, Tyutin, 1990) to the case under consideration. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The proposed scheme is applied to the quantization of a general quadratic theory. In addition, we consider the quantization of a damped oscillator and of a radiating point-like charge.Comment: 13 page

Dynamics of a Dirac Fermion in the presence of spin noncommutativity

Recently, it has been proposed a spacetime noncommutativity that involves spin degrees of freedom, here called "spin noncommutativity". One of the motivations for such a construction is that it preserves Lorentz invariance, which is deformed or simply broken in other approaches to spacetime noncommutativity. In this work, we gain further insight in the physical aspects of the spin noncommutativity. The noncommutative Dirac equation is derived from an action principle, and it is found to lead to the conservation of a modified current, which involves the background electromagnetic field. Finally, we study the Landau problem in the presence of spin noncommutativity. For this scenario of a constant magnetic field, we are able to derive a simple Hermitean non-commutative correction to the Hamiltonian operator, and show that the degeneracy of the excited states is lifted by the noncommutativity at the second order or perturbation theory.Comment: 18 pages, revtex

Deformation Quantization of a Certain Type of Open Systems

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators is discussed.Comment: Major update. Improved main statements. 21 page

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that actions of field theories on a noncommutative space-time can be written as some modified (we call them $\theta$-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and usual quantum mechanical features of the corresponding field theory. The $\theta$-modification for arbitrary finite-dimensional nonrelativistic system was proposed by Deriglazov (2003). In the present article, we discuss the problem of constructing $\theta$-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract $\theta$-modified actions of the relativistic particles from path integral representations of the corresponding noncommtative field theory propagators. We consider Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as $\theta$-modified actions of the relativistic particles. To confirm the interpretation, we quantize canonically these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The $\theta$-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case

Manifestation of triplet superconductivity in superconductor-ferromagnet structures

We study proximity effects in a multilayered superconductor/ferromagnet (S/F) structure with arbitrary relative directions of the magnetization ${\bf M}$. If the magnetizations of different layers are collinear the superconducting condensate function induced in the F layers has only a singlet component and a triplet one with a zero projection of the total magnetic moment of the Cooper pairs on the ${\bf M}$ direction. In this case the condensate penetrates the F layers over a short length $\xi_J$ determined by the exchange energy $J$. If the magnetizations ${\bf M}$ are not collinear the triplet component has, in addition to the zero projection, the projections $\pm1$. The latter component is even in the momentum, odd in the Matsubara frequency and penetrates the F layers over a long distance that increases with decreasing temperature and does not depend on $J$ (spin-orbit interaction limits this length). If the thickness of the F layers is much larger than $\xi_J$, the Josephson coupling between neighboring S layers is provided only by the triplet component, so that a new type of superconductivity arises in the transverse direction of the structure. The Josephson critical current is positive (negative) for the case of a positive (negative) chirality of the vector ${\bf M}$. We demonstrate that this type of the triplet condensate can be detected also by measuring the density of states in F/S/F structures.Comment: 14 pages; 9 figures. Final version, to be published in Phys. Rev.

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.Comment: New references added, Published online in Foundations of Physic

Negative ion surface-plasma source development for fusion in Novosibirsk

This paper is a review of research effected on negative ion plasma-surface sources in the Institute of Nuclear Physics in Novosibirsk. It contains the description of the performances of the planatron, a source which produced in 1972 in pure hydrogen a density of H- ion current of 0.75 A/cm2. The results of recent studies of this source, in the 1987 version, designated as semi-planatron, are also presented. The experiments effected by adding cesium to the hydrogen discharge lead to a theoretical model of the surface-plasma sources with low work function cathode. The optimization of the negative ion production led to the increase of the beam intensity to 11 A.Cet article présente une synthèse des travaux effectués à l'Institut de Physique Nucléaire de Novosibirsk sur les sources plasma-surface d'ions négatifs. Il contient la description des performances du planatron, une source qui a produit en 1972 une densité de courant d'ions H- de 0,75 A/cm2 en hydrogène pur. Les résultats des études de cette source dans sa version 1987, désignée semi-planatron, sont aussi présentés. Les expériences effectuées en ajoutant du césium à la décharge d'hydrogène ont conduit à l'élaboration d'un modèle théorique des sources plasma-surface à cathode à faible travail de sortie. L'optimisation de la production des ions négatifs a permis d'augmenter l'intensité du faisceau à 11 A

Interrelationship between anxiety and strategies of coping with exam stress: The role of gender, physiological indicators and sports

© 2020, Kazan Federal University. All rights reserved. The project studied the factors influencing the choice of students’ adaptation coping strategies for exam stress, namely, gender, physiology, anxiety, and sports. The study involved 139 healthy boy and girl student volunteers, both athletes and non-athletes, in their 1st and 2nd year of studies, aged between 18-22 years. It was conducted during the examinations with informed consent in accordance with the protocol № 6.26.06.2018, approved by the Local Ethics Committee. Stable relationships between anxiety and a number of physiological parameters were found: blood biochemistry, hormones and the functional state of the respiratory system. It showed that neither regular physical activities (sports) nor physiological parameters, affect the choice of coping strategy in the stressful situation of the exam and are not related to personal anxiety. Statistically significant differences were also found in the severity of reactive and personal anxiety in boys and girls, who used a number of coping strategies: “search for social support”, “acceptance of responsibility”, “flight-avoidance”. The article shows the correlation dependences between anxiety and physiological parameters and anxiety and coping strategies. The phenomenon of anxiety under examination stress is apparently a link between physiological parameters and behavior