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B. V. Novikov

Publications and source records attributed to B. V. Novikov.

13 recordsLinked to original sources
arXiv2016

Dispersion laws of the two-dimensional cavity magnetoexciton-polaritons

The energy spectrum of the 2D cavity magnetoexciton-polaritons has been investigated previously, using exact solutions for the Landau quantization of conduction electrons and heavy holes provided by the Rashba method [1]. Two lowest Landau quantization levels for electrons and three lowest Landau levels for heavy-holes, lead to the construction of the six lowest magnetoexciton sates. They consist of two dipole-active, two quadrupole-active, and the two forbidden quantum transitions from the ground state of the crystal to the magnetoexciton states. The interaction of the four optical-active magnetoexciton states with the cavity mode photons with a given circular polarization and with well-defined incidence direction leads to the creation of five magnetoexciton-polariton branches. The fifth order dispersion equation is examined by using numerical calculations and the second order dispersion equation is solved analytically, taking into account only one dipole-active magnetoexciton state. The effective polariton mass on the lower polariton branch, the Rabi frequency and the corresponding Hopfield coefficients are determined in dependence on the magnetic field strength, the Rashba spin-orbit coupling parameters and the electron and hole g-factors.

cond-mat.quant-gas↗
arXiv2014

Landau quantization, Rashba spin-orbit coupling and Zeeman splitting of two-dimensional heavy holes

The origin of the g-factor of the two-dimensional (2D) electrons and holes moving in the periodic crystal lattice potential with the perpendicular magnetic and electric fields is discussed. The Pauli equation describing the Landau quantization accompanied by the Rashba spin-orbit coupling (RSOC) and Zeeman splitting (ZS) for 2D heavy holes with nonparabolic dispersion law is solved exactly. The solutions have the form of the pairs of the Landau quantization levels due to the spinor-type wave functions. The energy levels depend on amplitudes of the magnetic and electric fields, on the g-factor {g-h}, and on the parameter of nonparabolicity C. The dependences of two energy levels in any pair on the Zeeman parameter {Z_h}={g_h}{m_h}/4{m_0}, where {m_h} is the hole effective mass, are nonmonotonous and without intersections. The smallest distance between them at C=0 takes place at the value {Z_h}=n/2, where n is the order of the chirality terms determined by the RSOC and is the same for any quantum number of the Landau quantization.

cond-mat.str-el↗
arXiv2014

Bose-Einstein Condensation of two-dimensional polaritons in microcavity under the influence of the Landau quantization and Rashba spin-orbit coupling

The Bose-Einstein condensation (BEC) of the two-dimensional (2D) magnetoexciton-polaritons in microcavity, when the Landau quantization of the electron and hole states accompanied by the Rashba spin-orbit coupling plays the main role, were investigated. The Landau quantization levels of the 2D heavy holes with nonparabolic dispersion law and third order chirality terms both induced by the external electric field perpendicular to the semiconductor quantum well as the strong magnetic field B gives rise to the nonmonotous dependence on B of the magnetoexciton energy levels and of the polariton energy branches. The Hamiltonian describing the Coulomb electron - electron and the electron - radiation interactions was expressed in terms of the two-particle integral operators such as the density operators $\hatρ(\vec{Q})$ and $\hat{D}(\vec{Q})$ representing the optical and the acoustical plasmons and the magnetoexciton creation and annihilation operators $Ψ_{ex}^{\dagger}({\vec{k}_{||}}),Ψ_{ex}^{}({\vec{k}_{||}})$ with in - plane wave vectors ${\vec{k}_{||}}$ and $\vec{Q}$. The polariton creation and annihilation operators $L_{ex}^{\dagger}({\vec{k}_{||}}),L_{ex}^{}({\vec{k}_{||}})$ were introduced using the Hopfield coefficients and neglecting the antiresonant terms because the photon energies exceed the energy of the cavity mode. The BEC of the magnetoexciton - polariton takes place on the lower polariton branch in the point ${\vec{k}_{||}}=0$ with the quantized value of the longitudinal component of the light wave vector, as in the point of the cavity mode.

cond-mat.str-el↗
arXiv2008

On 0-homology of categorical at zero semigroups

The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.

math.KT↗
arXiv2008

0-Cohomology of semigroups

This article is a survey of 0-cohomology of semigroups. The main attention is devoted to applications.

math.RA↗
arXiv2008

Semigroup cohomology and applications

This article is a survey of the author's research. It consists of three sections concerned three kinds of cohomologies of semigroups. Section 1 considers `classic' cohomology as it was introduced by Eilenberg and MacLane. Here the attention is concentrated mainly on semigroups having cohomological dimension 1. In Section 2 a generalization of the Eilenberg-MacLane cohomology is introduced, the so-called 0-cohomology, which appears in applied topics (projective representations of semigroups, Brauer monoids). At last Section 3 is devoted to further generalizing: partial cohomology defined and discussed in it are used then for calculation of the classic cohomology for some semigroups.

math.RA↗
arXiv2008

Finitary incidence algebras

We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical, idempotents, regular elements. As a consequence a positive solution of the isomorphism problem for such algebras is obtained.

math.RA↗
arXiv2008

On quasi-Frobenius semigroup algebras

We define quasi-Frobenius semigroups and find necessary and sufficient conditions under which a semigroup algebra of a 0-cancellative semigroup is quasi-Frobenius.

math.RA↗
arXiv2008

Semigroup cohomology as a derived functor

In this work we construct an extension for the category of 0-modules by analogy with [H.-J. Baues and G. Wirshing, Cohomology of small categories, J. Pure Appl. Algebra, 38(1985), 187-211]. The 0-cohomology functor becomes a derived functor in the extended category. As an application of this construction we calculate the cohomological dimension of so-called 0-free monoids.

math.CT↗
arXiv2008

On the Brauer monoid for finite fields

The Brauer monoid is studied by the notion of 0-cohomology. We investigate the impact of invertible elements of modifications on the structure of the Brauer monoid, especially for finite fields.

math.GR↗