Energy-band structure of semiconductors having the chalcopyrite lattice

The pseudopotential method is used to calculate the band structure of semiconductors having the chalcopyrite lattice. Calculations are carried out for the most important symmetry points of the Brillouin zone. The band structure of ZnSiP₂ is calculated, and the results are used in a discussion of the electric and optical properties of this substance.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 58–66, November, 1969.     

Energy-band structure of semiconductors having the chalcopyrite lattice

The pseudopotential method is used to calculate the band structure of several A^IIB^IVC^V semiconductors. The calculations are carried out at the most important symmetry points of the Brillouin zone: , T, N, and P. The top of the valence band and the bottom of the conduction band are shown to correspond to point . The dispersion law near is described approximately by the Kane equations.Translated from Izvestiya VUZ. Fizika, No. 7, pp. 17–22, July, 1970.     

Dynamics of the calcium lattice

The normal vibration modes of the calcium lattice are calculated. The elastic moduli and Debye temperature are evaluated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 83–86, October, 1970.     

Dynamics of a lattice gas

A stochastic model whose ergodic variant coincides with the Ising model has been considered. Constraints following from a microscopic conservation law are imposed on dynamics (lattice gas model). The master equation for the dynamic correlation function has been derived. It has been shown that the separation curve on the density-temperature diagram for the initial microdispersed state lies below that predicted by the Gibbs statistics. Furthermore, not only the position but also the shape of the entire curve can change: it becomes double humped rather than dome shaped.     

The theory of infrared dispersion of light in crystals with chalcopyrite lattice

The low-frequency dielectric tensor is calculated for A^IIB^IVC ₂ ^V and A^IB^IIIC ₂ ^VI crystals in terms of the long-wave frequencies of lattice vibrations, corresponding to various orientations of the wave vector. The qualitative shape of the spectrum of mechanical polaritons is obtained. The coefficient of light reflection is calculated as a function of the frequency and direction of propagation for a CdGeP₂ crystal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 39–43, June, 1978.     

Dynamics of the BiTeI lattice at high pressures

Raman measurements of the phonon spectrum of BiTeI at pressures of up to 20 GPa have been performed. A decrease in the linewidth of E² vibration by almost a factor of 2 with an increase in the pressure to 3 GPa has been detected. The frequencies of all four Raman active modes increase monotonically with the pressure. These lines are observed in spectra up to ～8 GPa. Sharp change in the spectrum occurs at pressures of 8–9 GPa, indicating a transition to the high-pressure phase, which holds up to 20 GPa. This transition is reversible and hardly has any hysteresis. A sample in the high-pressure phase is single crystal.     

Dynamics in a lattice epidemic model

We present a lattice-based epidemic model of a nonfatal communicable disease in a mobile host population in which novel dynamical behaviour is observed. The model exhibits temporal and spatial fluctuations over a wide range of time scales with a power spectrum of 1/ƒ^1.2 form. The consequences of this scaling behaviour for prevalence of endemic disease is discussed.     

On kinetic phenomena in semiconducting compounds of AIBIIIC2 VI type with chalcopyrite lattice

A four-ellipsoid model of the vertex of the valence band, proposed earlier for some semiconducting compounds of type A^IB^IIIC₂ ^VI, is examined. The anisotropy of the galvano- and thermomagnetic effects is studied under the assumption of an anisotropic relaxation time and the presence of one scattering mechanism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–51, July, 1973.     

Dynamics of fluctuations for quantum lattice systems

For short range interactions and forL ¹-space clustering states it is proved that there exists a bonafide time evolution on the set of normal fluctuations. This dynamics is applied to derive the notion of equilibrium state of the algebra of fluctuations.     

Dynamics of the lattice of magnetic nanodipoles with cubic anisotropy

The 5 × 5 square lattices of magnetic dipoles with cubic crystallographic anisotropy were investigated by the computer simulation method. The conditions for implementing the random orientation of lattice configurations, each of which are characterized by a certain response to the influence of an external magnetic pulse, as well as by the established regime of the oscillation of the total magnetic moment under the influence of an alternating field, are revealed. Regular vibration modes with a doubled frequency and quasi-periodic and chaotic modes are detected. The dependence of the system response on the parameters of the magnetic field pulse is studied.     

Dynamics of kicked matter-wave solitons in an optical lattice

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in an optical lattice. The resulting soliton’s dynamics is studied within the framework of the time-dependent nonpolynomial Schrödinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.     

Energy band structures of the chalcopyrite lattice semiconductors CuAlS2, CuAlSe2, CuInS2, and CuInSe2

The pseudopotential method is used to calculate the energy band structures of four -type semiconductors including the effect of the displacement of anions from face-centered sites in the sublattices. It was established that CuAlSe₂, CuInS₂, and CuInSe₂ are direct gap semiconductors and that CuAlS₂ has a pseudodirect energy gap. Experimental data derived from studies of the optical properties of these crystals in the U V region are also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–12, June, 1976.     

Dynamics and control of oscillations in a complex crystalline lattice

A highly nonlinear system of acoustic and optical oscillations in a complex crystalline lattice consisting of two sublattices is analyzed. The system is obtained as a generalization of the linear Carman–Born–Kun Huang theory. Large displacements of atoms up to structure stability loss and restructuring are admitted. It is shown that the system has nontrivial solutions describing movements of fronts, emergence of periodic structures and defects. Strong interaction of acoustic and optical modes of oscillation for media without center of symmetry is demonstrated. A possibility of energy-excitation of the optical mode by means of controlling torque applied to the ends of the lattice is examined. Control algorithm based on speed-gradient method is proposed and analyzed numerically. Simulation results demonstrate that application of control may eliminate or reduce influence of initial conditions. An easily realizable nonfeedback version of control algorithm is proposed possessing similar properties.     

Energy-band structure of semiconductors having the chalcopyrite lattice II. MgSiP2, ZnGeP2, ZnSiAs2, and CdSiP2

The pseudopotential method is used to calculate the band structure of MgSiP₂, ZnGeP₂, ZnSiAs₂, and CdSiP₂. The valence band of these compounds is shown to consist of several allowed subbands separated by energy gaps. There are two levels at the top of the valence band, slightly separated in ZnGeP₂ and ZnSiAs₂ and well-separated in MgSiP₂ and CdSiP₂ — in which there is significant tetragonal compression of the lattice. The effective electron masses at the bottom of the conduction band turn out to be anisotropic, with m/m 7–10.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 95–100, June, 1970.     

Dynamics of Bose-Einstein condensates in a one-dimensional optical lattice with double-well potential

We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π-mode self-trapping regime.