arXiv subjects

V. G. Bagrov

Publications and source records attributed to V. G. Bagrov.

28 records · Page 2Linked to original sources

arXiv2004

Darboux transformation for two-level systems

We develop the Darboux procedure for the case of the two-level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two-level system, transforming only one real potential into another real potential. We apply the obtained Darboux transformation to known exact solutions of the two-level system. Thus, we find three classes of new solutions for the two-level system and the corresponding new potentials that allow such solutions.

math-ph↗

arXiv2002

Angular dependence of synchrotron radiation intensity

The detailed analysis of angular dependence of the synchrotron radiation (SR) is presented. In particular, we analyze the angular dependence of the integral SR-intensity and peculiarities of the angular dependence of the first harmonics SR. Studying spectral SR-intensities, we have discovered their unexpected angular behavior, completely different from that of the integral SR-intensity. Namely, for any given synchrotron frequency, maxima of the spectral SR-intensities recede from the orbit plane with increasing particle energy. Thus, in contrast with the integral SR-intensity, the spectral ones have the tendency to deconcentrate themselves on the orbit plane.

physics.acc-ph↗

arXiv2002

Solutions of relativistic wave equations in superpositions of Aharonov-Bohm, magnetic, and electric fields

We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some additional electric and magnetic fields. In particular, as such additional fields, we consider longitudinal electric and magnetic fields, some crossed fields, and some special non-uniform fields. The solutions obtained can be useful to study Aharonov-Bohm effect in the corresponding electromagnetic fields.

hep-th↗

arXiv2001

Aspects of Two-Level Systems under External Time Dependent Fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility to directly apply powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for ``quantum chaos'' when the external background is periodic or quasi-periodic in time.

quant-ph↗

arXiv2001

New solutions of relativistic wave equations in magnetic fields and longitudinal fields

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest. Namely, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.

hep-th↗

arXiv2000

Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations

We study the impact of Aharonov-Bohm solenoid on the radiation of a charged particle moving in a constant uniform magnetic field. With this aim in view, exact solutions of Klein-Gordon and Dirac equations are found in the magnetic-solenoid field. Using such solutions, we calculate exactly all the characteristics of one-photon spontaneous radiation both for spinless and spinning particle. Considering non-relativistic and relativistic approximations, we analyze cyclotron and synchrotron radiations in detail. Radiation peculiarities caused by the presence of the solenoid may be considered as a manifestation of Aharonov-Bohm effect in the radiation. In particular, it is shown that new spectral lines appear in the radiation spectrum. Due to angular distribution peculiarities of the radiation intensity, these lines can in principle be isolated from basic cyclotron and synchrotron radiation spectra

hep-th↗

arXiv1998

Darboux transformation of coherent states

It is proved that the Darboux transformation of the system of coherent states of a free particle leads to the states that may be treated as coherent states of soliton-like potentials.

math-ph↗

arXiv1998

Semiclassical trajectory-coherent approximation in quantum mechanics: II. High order corrections to the Dirac operators in external electromagnetic field

High approximations of semiclassical trajectory-coherent states (TCS) and of semiclassical Green function (in the class of semiclassically concentrated states) for the Dirac operator with anomalous Pauli interaction are obtained. For Schrodinger and Dirac operators trajectory-coherent representations are constructed up to any precision with respect to h, h-->0.

quant-ph↗

arXiv1997

The quantum effects in the undulator of infinite length

The first order quantum correction to the power of spontaneous radiation of electrons in an arbitrary two-component periodic magnetic field was obtained. The phenomenon of selfpolarization of the spin of electrons in a process of spontaneous radiation was also studied. By electron's motion in a spiral magnetic undulator, the quantitative characteristics of selfpolarization (the polarization degree and the relaxation time) are different from corresponding ones in synchrotron radiation. The limiting cases of near-axis and ultrarelativistic approximation were considered.

quant-ph↗

arXiv1994

On the possible experimental manifestations of the torsion field at low energies

We construct the theoretical base for the search of the possible experimental manifestations of the torsion field at low energies. The weakrelativistic approximation to the Dirac equation in an external torsion field is considered. For the sake of generality we introduce the external electromagnetic field in parallel. The generalized (due to torsion dependent terms) Pauly equation contains new terms which have the different structure if compared with standard electromagnetic ones. Just the same takes place for the weakrelativistic equations for spin $\frac{1}{2}$ particle in an external torsion and electromagnetic field. It is given the brief description of the possible experiments.

hep-th↗