arXiv subjects
Publications and source records attributed to I. V. Kozlov.
A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of the expectation for each summand: the members of an ``infrequent'' part of the whole sequence may have moments of orders converging to zero.
A strong law of large numbers (SLLN) for sublinear expectation under a certain integrability condition is proved. It is shown that the proposed integrability condition is weaker than the majorant condition introduced by Cheng Hu (2018). The proof is based on the truncation method of N. Etemadi (1981).
Properties of the boundary of two conductors in a quantizing magnetic field are studied: with conventional Dirac charge carriers and so-called pseudospin-1 fermions, which are realized in graphene-like and Lieb lattices respectively. It is shown that edge states arise that relate the properties of conductors to the trivial and nontrivial Berry phase. These edge states lead to the appearance of a characteristic series of root features in the density of states.
Effects associated with the interference of electron waves around a magnetic point defect in two-dimensional electron gas with combined Rashba-Dresselhaus spin-orbit interaction in the presence of a parallel magnetic field are theoretically investigated. The effect of a magnetic field on the anisotropic spatial distribution of the local density of states and the local density of magnetization is analyzed. The existence of oscillations of the density of magnetization with scattering by a non-magnetic defect and the contribution of magnetic scattering (accompanied by spin-flip) in the local density of electron states are predicted.
Spin orbit interaction (SOI) having a complicated energy spectrum with a conical point and four critical points are promising candidates to observe electron topological transitions. In the present paper we have investigated the evolution of the electron spectrum and isoenergetic contours under the influence of parallel magnetic field. General formulas for energies of critical points for arbitrary values of SOI constants and magnetic field are found. The existence of critical magnetic fields at which a number of critical points is changed has been predicted. The magnetic field driving topological Lifshitz transitions in the geometry of isoenergetic contours have been studied. Van Hove's singularities in the electron density of states are calculated. The obtained results can be used for theoretical investigations of different electron characteristics of such 2D systems.
New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba - Dresselhaus spin - orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that allows an exact analytical solution is also highlighted. To demonstrate the advantages of our approach we apply the obtained Green's function to calculation of electron density and magnetization