https://elib.bsu.by:443/handle/123456789/162703 NPCS Vol.18, no.2, pp. 105-283 (2015) Mon, 20 Apr 2026 12:13:44 GMT 2026-04-20T12:13:44Z https://elib.bsu.by:443/handle/123456789/163116 Заглавие документа: Semimetals with Fermi Velocity A˙ected by Exchange Interactions: Two Dimensional Majorana Charge Carriers Авторы: Grushevskaya, H. V.; Krylov, G. Аннотация: A theoretical approach to the band theory of two-dimensional (2D) semimetals within the self-consistent Dirac–Hartree–Fock field approximation has been developed. It reveals partially breaking symmetry of Dirac cone a˙ected by quasi-relativistic exchange interactions for 2D crystals with hexagonal symmetry. Fermi velocity becomes an operator within this approach, elementary excitations are three-particle fermionic excitons described by Majorana rather than Dirac equation. Such features of the band structure of 2D semimetals as appearance of 4 pairs of Weyl-like nodes and Dirac cone replicas is shown to be naturally explained with the developed formalism. Thu, 01 Jan 2015 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/163116 2015-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/163114 Заглавие документа: Effect of Weak Dissipation on The Dynamics of Multidimensional Hamiltonian Systems Авторы: Felk, E. V.; Savin, A. V.; Kuznetsovy, A. P. Аннотация: We discuss the effect of weak dissipation on the system with Arnold diffusion which consists of two coupled twist maps. The finite time Lyapunov exponents are used to analyze the dynamics. We observe the phenomenon of transient chaos and changes in the phase space structure including the disappearance of some resonances. Thu, 01 Jan 2015 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/163114 2015-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/163113 Заглавие документа: Spin 1 Particle in the Magnetic Monopole Potential for Minkowski and Lobachevsky Spaces: Nonrelativistic Approximation Авторы: Veko, O. V.; Kazmerchuk, K. V.; Ovsiyuk, E. M.; Kisel, V. V.; Ishkhanyan, A. M.; Red’kov, V. M. Аннотация: The spin 1 particle is treated in the presence of the Dirac magnetic monopole in the Minkowski and Lobachevsky spaces. Separating the variables in the frame of the matrix 10-component Duffin–Kemer–Petiau approach and making a nonrelativistic approximation in the corresponding radial equations, a system of three coupled second order linear differential equations is derived for each type of geometry. For the Minkowski space, the nonrelativistic equations are disconnected using a linear transformation, which makes the mixing matrix a diagonal one. The resultant three unconnected equations involve three roots of a cubic algebraic equation as parameters. The approach allows extension to the case of additional external spherically symmetric fields. The Coulomb potential is considered and three series of energy spectra are derived. Special attention is given to the states with minimum value of the total angular momentum. In the case of the curved background of the Lobachevsky geometry, the mentioned linear transformation does not disconnect the nonrelativistic equations in the presence of the monopole. Nevertheless, we derive the solution of the problem in the case of minimum total angular momentum and in presence of the Coulomb field. Finally, considering the case without the monopole field, we show that for Coulomb potential the problem is reduced to a system of three differential equations involving a hypergeometric and two general Heun equations. Imposing on the parameters of the latter equations a specific requirement, reasonable from the physical standpoint, we derive the corresponding energy spectra. Thu, 01 Jan 2015 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/163113 2015-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/162933 Заглавие документа: Nonlinear Waves as Signals in Microtubules Авторы: Bugay, A. N. Аннотация: Modern models predict phenomena of nonlinear elastic waves propagation within cellular microtubules. But little is known about their interaction with near environment such as ionic shell in solution. In present paper a model of localized nonlinear electro-acoustic wave excitation is proposed and kink solution is obtained. The kink transfers internal bending of tubulin dimers with synchronous electric current of condensed counterions along microtubule. Suggested mechanism of active wave propagation relies on energy supply by GTP hydrolysis. Thu, 01 Jan 2015 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/162933 2015-01-01T00:00:00Z