Canonical formulation of the theory of a free integral-spin massive field

A Lagrangian is constructed for free integral-spin massive fields in space — time of arbitrary dimension. The Hamiltonian of the theory is found and the structure and algebra of the couplings are established.Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 100–105, February, 1995.     

Spontaneous parametric transition from periodic motion to chaos in a dynamical system with two degrees of freedom

A study is made of a spontaneous parametric transition to chaos by the disruption of periodic motion in a generating structure with two degrees of freedom. A comparison of the properties of the system examined in this study and the properties of objects with an infinite-dimensional phase space shows the universality of the spontaneous parametric scenario for a loss of stability of periodic motion that leads to randomization of the oscillatory process. Tomsk University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. 2, pp. 91–95, February, 1999.     

Quasi-energy states and asymptotics uniform in time

It is shown that quasiclassical asymptotics uniform in time can be constructed for quantum systems with periodic Hamiltonian. Quasi-energy spectral series of states in an axially symmetric electromagnetic field and the field of a plane electromagnetic wave are constructed. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, pp. 24–30, No. 7, July, 1999.     

Cosmological solution of the Einstein—Weyl equation

The accurate integration of the Einstein—Weyl field equations is considered for the case when the spinor field depends only on the time, while the metric specifies a uniform space—time of type I in the Bianci classification, i.e., a particular case of a Steckel space of type (3.0). Tomsk State Pedagogical University. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 69–78, November, 1998.     

Some new systems that generate a uniform stochastic web

Evidence is given that many classes of periodically kicked Hamiltonian system with 1.5 degree of freedom generate infinite, uniform stochastic webs. The kick term in the Hamiltonian or the equation of motion need not be purely sinusoidal or some small perturbation of a sinusoidal function. For the resonance condition q=4 the structure of the web can be different from a square lattice; However, remarkably symmetric patterns of chaos are still present throughout the whole phase space. Examples are given for the square wave function and sawtooth function in the kick term of the equation of motion. The sensitive dependence on initial conditions of those systems is investigated.     

Darboux transformation of the coherent states of a nonrelativistic free particle

Various systems of soliton-potential coherent states have been derived. Measures are found that realize the expansion of a unit operator in terms of projectors on these states. Two different realizations of Hilbert state space are constructed as functions holomorphic throughout the complex plane and with a certain constraint on their increase. Tomsk State University and Tomsk State Pedagogic University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. 2, pp. 19–25, February, 1999.     

Classification of conformal steckel spaces in the vaidia problem

The classification of isotropic conformal Steckel spaces satisfying a system of Einstein equations in which the right-hand side is the energy—momentum tensor of an isotropic ideal liquid is considered. The complete solution of the problem is found for the case of a conformal Steckel space admitting of one isotropic Killing vector field and two Killing tensor fields, when these objects form a complete set. Tomsk State University. Tomsk State Pedagogical University. Institute of High-Power Electronics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 48–53, August, 1996.     

Hamiltonian approach to the dynamics of a chemostat

Based on the Hamiltonian approach to an analysis of the system of Monod equations describing the chemostat dynamics, their partial analytical solution is found for a certain class of initial conditions. It is shown that this class of initial conditions can be easily realized in microbiological practice, and the solution obtained is generally described by the attractor of the system trajectories. A methodical approach, which allows the given Hamiltonian formalism to be used to analyze the kinetics of growth of microorganisms in the chemostat, is developed and experimentally checked. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 2000.     

Darboux transformation of coherent states for a Lobachevski plane

A Darboux transformation of coherent states is considered for a singular oscillator. A coordinate representation and a holomorphic representation are obtained for the Darboux transformation operator and the coherent states. The Hermitian metric and the Kaler potential of the transformed system are calculated. It is established that a Darboux transformation corresponds to curvature of the phase space of the classical system. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–36, September, 1997.     

Isotropic Steklov-conformal metrics of plane-conformal spaces

An explicit form is found for metrics that allow integration of geodesic equations for massless particles in plane-conformal spaces by complete separation of the variables in the Hamilton-Jacobi equations. Tomsk University and Tomsk State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 92–96, November, 1998.     

Formation and development of laser physics at Tomsk University

The formation of the laser school in the Siberian Physical-Technical Institute at Tomsk State University is considered in historical perspective. The most important achievements and publications are discussed. The role of Siberian Conferences on Spectroscopy held regularly under the supervision of Prof. N.A. Prilezhaeva in the development of laser physics at Tomsk University and in the city of Tomsk is demonstrated. Tomsk State University; the V. D. Kuznetsov Siberian Physical-Technical Institute at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 4–13, August 1999.     

Formation of a transition layer during heteroepitaxy of III–V compound semiconductors in gas-phase epitaxy systems

It is known that during gas-phase epitaxy of InP and GaAs the region of the film close to the heteroboundary is formed with altered phase, structural, and electrophysical properties. The main cause for this is formation of a transition layer due to a change in the growth mechanism (transition from nucleational to layer-step growth) and the structure of the growing surface (height and density of growth steps). Tomsk State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. 1, pp. 18–21, January, 1999.     

Accurate integration of scalar equations in multiscalar-tensor theory

The integration of scalar equations in theories generalizing Brans—Dicke—Jordan—Fierz scalar—tensor theory is considered. Conditions under which these equations may be integrated by complete variable separation are established. Under these conditions, the scalar equations take the form of classical equations of motion for a single particle moving in scalar space in an external force field.Institute of High-Power Electronics, Siberian Branch, Russian Academy of Sciences. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 79–84, February, 1995.     

A minimax approach in the theory of the excited states of many-electron systems

Theorems are stated and proved that allow one to determine the saddle points of energy functionals for excited states and to select the particular saddle point that provides a improvable upper bound to the characteristic eigenvalue of the Hamiltonian. A general minimax approach, based on the proved theorems, is proposed for calculating the excited states of many-electron systems having lower-lying states of the same symmetry.Tomsk Pedagogical Institute. V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 35–41, November, 1992.     

Small polaron dynamics: A self-consistent nonlinear spin-field model

The motion of an electron strongly and locally coupled to the lattice deformation is considered as a dynamical system. Our study is based on a model where the electron remains to two adjacent diatomic molecules vibrating around positions which evolve in time as the charge distribution of the electron gradually shifts from one of the molecules to the other one. This model is cast into an intuitively more accesible model of spin $\text{1}\text{2}$ in an external field plus a reaction field. Within a semiclassical approach this is a Hamiltonian system expressed with two sets of action-angle variables. We show how the regular trajectories (describing the cooperative mechanism between the charge transfer and rearrangement of the molecular positions) in this phase space gradually disappear and global stochasticity sets in as either the ratio of the electron hopping rate over the electron-lattice coupling constant or the total energy is varied.     

Motion of vortices outside a cylinder

The problem of motion of the vortices around an oscillating cylinder in the presence of a uniform flow is considered. The Hamiltonian for vortex motion for the case with no uniform flow and stationary cylinder is constructed, reduced, and constant Hamiltonian (energy) curves are plotted when the system is shown to be integrable according to Liouville. By adding uniform flow to the system and by allowing the cylinder to vibrate, we model the natural vibration of the cylinder in the flow field, which has applications in ocean engineering involving tethers or pipelines in a flow field. We conclude that in the chaotic case forces on the cylinder may be considerably larger than those on the integrable case depending on the initial positions of vortices and that complex phenomena such as chaotic capture and escape occur when the initial positions lie in a certain region.     

Radiation by relativistic dipoles. III

The classical radiation of a point magnetic moment (a magneton) moving at a constant velocity in an arbitrary direction with respect to the field lines of a uniform magnetic field is analyzed. All characteristics of the radiation agree with the Ternov-Bagrov-Khapaev relativistic quantum thoery of the radiation by a neutron. It is thus demonstrated that the classical model of radiation with spin flip is valid. The correspondence principle in the theory of radiation with spin flip will be discussed in more detail in subsequent papers.V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 53–59, January 1994.     

Method of kinematic projecting of pulsar-emission profiles

A method for constructing profiles of incoherent pulsar emission based on the instantaneous angular phase distribution function of radiant power emitted by a relativistic source that moves in the magnetosphere of a neutron star is suggested. In general, this phase function depends on the kinematic parameters of the radiation source (its velocity and acceleration) and on the direction of radiation emission with respect to the rotating neutron star (the observation direction). The method is illustrated by the example of calculated profiles of fan pulsar radiation with the use of the phase function of synchrotron radiation. It is stated that his method can easily be generalized for other types of relativistic radiation. Tomsk State University; Tomsk State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 26–31, January, 2000.     

Action-angle variables in the theory of superconductivity and superfluidity phenomena

The problem of two bodies that interact in such a way that they describe a rotational motion in Euclidean (pseudo-Euclidean) space is considered within the framework of a classical-mechanics formalism. It is shown on the basis of the Hamiltonian equations of motion that the system can be described in action-angle variables. While not planar, its phase space exhibits the properties of a Köhler manifold, which permits exact quantization of the classical system. The results of quantization are easily identified with known quantum models that describe superconductivity and superfluidity phenomena, making it possible to transfer the properties of the classical system to those of the quantum system, whose evolution can therefore also be described in action-angle variables.