The BMV-conjecture over quaternions and octonions

This paper investigates generalizations of the BMV-conjecture for quaternionic and octonionic matrices. For quaternions the correctness of the formulation is shown as well as its equivalence to the original conjecture for complex matrices. General properties of octonions and Hermitian matrices over them are examined for the BMV-conjecture formulation over octonions.     

On the problem of propagation of nonlinear coupled TE-TM waves in a layer

The problem of simultaneous propagation of two types of electromagnetic waves (TE and TM) in a plane dielectric waveguide filled with a nonlinear medium is considered. These polarized waves have different frequencies and different propagation constants. The physical problem is reduced to a nonlinear two-parameter transmission eigenvalue problem for Maxwell’s equations in a layer. The coupled eigenvalues are coupled propagation constants. A theorem on the existence and localization of coupled eigenvalues corresponding to coupled polarized electromagnetic waves is proved.     

Necessary first-order conditions for optimal crossing of a given region

We consider a nonlinear optimal control problem with an integral functional in which the integrand is the characteristic function of a closed set in the phase space. An approximation method is applied to prove the necessary conditions of optimality in the form of a Pontryagin maximum principle without any prior assumptions on the behavior of the optimal trajectory. Similarly to phase-constrained problems, we derive conditions of nondegeneracy and pointwise nontriviality of the maximum principle. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 179–204, 2004.     

Spectral properties of one-dimensional disperse crystals

The connection between the spectral characteristics of the one-dimensional Schrödinger operator with periodic potential, asa, and the spectral characteristic of the Schrödinger operatorl(y)=–y+q(x)y with a decreasing potentialq(x) is studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 197–211, 1984.     

Electron-impact excitation of the 3 P o and 3 D o levels of a nickel atom

The excitation cross sections of transitions from the ³ P ^o and ³ D ^o levels of a nickel atom in electron-atom collisions at an exciting-electron energy of 50 eV have been analyzed by the method of extended crossing beams with detection of the optical signal from excited atoms. Eleven optical excitation functions have been recorded in the electron-energy range of 0?C200 eV. The direct excitation cross sections of the energy levels and the contribution of the cascade transitions were calculated using the data obtained.     

Experimental study of mode selection in shallow-water sea

The possibilities of matching low-frequency underwater sound pulses to the parameters of an oceanic waveguide are considered. The objective is to optimize the system of few-mode tomographic observation in a shallow-water sea. Experimental data are analyzed for two methods of selecting the low-frequency fewmode pulses propagating in a shallow-water sea. The first method excites probe pulses by vertically elongated arrays, with spatial filtering after vertical or horizontal arrays receive the pulses. The second method is based on exciting broadband signals with linear frequency modulation by a single transmitter. The selection of the few-mode signal is performed by time strobing the signals at the output of the matched filter after a horizontal array receives the pulses. The distance between the sound sources and receiving systems varied from 10 to 300 km.     

Polarization locking and nonparaxial spatial solitons in media with electronic Kerr nonlinearity

The polarization structure of nonparaxial spatial solitons in a transparent medium with the electronic mechanism of Kerr nonlinearity is studied theoretically. It is demonstrated analytically in the weak nonparaxiality approximation that the regime of polarization locking, in which all the field components have the same propagation constant, is the only stable regime. Estimates of the rate of transition of the initial metastable regime of rotation of the polarization ellipse to the regime of polarization locking are presented. Based on a numerical solution of the nonlinear Maxwell equations, the presence of the nonparaxial regime of polarization locking is confirmed and the main characteristics of the corresponding spatial solitons are obtained.     

Optical amplification of photoinduced polarizability gratings in phosphate glasses

It is experimentally demonstrated that second-order polarizability gratings preliminarily recorded using bichromatic light in a phosphate glass can be amplified under the action of monochromatic radiation. The amplification effect takes place irrespective of the polarization and direction of propagation of the amplifying radiation and is achieved at various wavelengths. The phenomenon is related to the asymmetry of optical transitions between local centers in an isotropic medium in the presence of electric field. It is theoretically shown that this system may feature the formation of alternating electric field domains with dimensions depending on the grating amplitude.     

Manifestation of a semimetallic state in cyclotron resonance in low-symmetry HgTe-based quantum wells

Cyclotron-resonance measurements in 21-nm-thick HgTe/CdHgTe quantum wells of different crystallographic orientations have been performed. It has been found that, in contrast to the structures with the (001) orientation of the quantum-well plane, (013)-oriented quantum wells are semimetallic and their absorption spectra exhibit both electron and hole cyclotron-resonance lines. The simultaneous presence of the two types of charge carriers originates from an overlap between the upper heavy-hole quantum-confinement subbands hh1 and hh2. This overlap is caused by the strong interaction of these subbands with the Dyakonov-Khaetskii interface state. Calculations carried out using the eight-band kp-Hamiltonian indicate that, for known values of the band-structure parameters, the overlap between hh2 and hh1 subbands does not occur; this result is in agreement with the cyclotron-resonance data for (001)-oriented structures. The enhanced interaction between heavy-hole and interface states owing to the existence of steps at low-symmetry heterointerfaces may be the mechanism responsible for the appearance of an overlap between subbands in HgTe quantum wells with orientation different from (001).