Drazin-Star and Star-Drazin Inverses of Bounded Finite Potent Operators on Hilbert Spaces

The aim of this work is to extend to bounded finite potent endomorphisms on arbitrary Hilbert spaces the notions of the Drazin-Star and the Star-Drazin of matrices that have been recently introduced by D. Mosić. The existence, structure and main properties of these operators are given. In particular, we obtain new properties of the Drazin-Star and the Star-Drazin of a finite complex matrix. Moreover, the explicit solutions of some infinite linear systems on Hilbert spaces from the Drazin-Star inverse of a bounded finite potent endomorphism are studied.

Two-level systems coupled to Graphene plasmons: A Lindblad equation approach

In this paper, we review the theory of open quantum systems and macroscopic quantum electrodynamics, providing a self-contained account of many aspects of these two theories. The former is presented in the context of a qubit coupled to a electromagnetic thermal bath, the latter is presented in the context of a quantization scheme for surface-plasmon polaritons (SPPs) in graphene based on Langevin noise currents. This includes a calculation of the dyadic Green’s function (in the electrostatic limit) for a Graphene sheet between two semi-infinite linear dielectric media, and its subsequent application to the construction of SPP creation and annihilation operators. We then bring the two fields together and discuss the entanglement of two qubits in the vicinity of a graphene sheet which supports SPPs. The two qubits communicate with each other via the emission and absorption of SPPs. We find that a Schrödinger cat state involving the two qubits can be partially protected from decoherence by taking advantage of the dissipative dynamics in graphene. A comparison is also drawn between the dynamics at zero temperature, obtained via Schrödinger’s equation, and at finite temperature, obtained using the Lindblad equation.

FILTERING CALCULATIONS OF WATERLOWERING IN THE CONSTRUCTION OF ENGINEERING COMMUNICATIONS

The purpose of the investigations is an assessment of filtration calculations of water lowering during construction works and laying engineering communications at the water catchment of the Likhoborka and Zhabenka rivers. There are considered hydrogeological questions of filtration calculations at construction and laying urban and rain sewers on the territory of the Dmitrovskoe highway in the Northern administrative district of Moscow. It is revealed that the main factors affecting hydrogeological conditions in the area of construction of engineering communications is water lowering. The dependences on the estimation of filtration calculations of water lowering in the area of construction of engineering communications are analyzed. Analytical dependences for the scheme of an infinite linear source of perturbation in the infinite layer are proposed and improved. It is established that the average costs are proportionally dependent to the level of water lowering in the water lowering area,and the relationship between average costs, regardless of the calculated linear scheme, is linear. A model for filtration calculations has been developed in Microsoft Excel. The model calculations showed that the maximum decrease in the estimated point of a multi-story non-residential administrative building does not exceed the values of the maximum allowable deformations.

New insights into the 1D carbon chain through the RPA

Using correlated wave function based methods, the modeling of promising new materials is elevated to a new level. For the first time, a realistic phonon dispersion relation is predicted for the infinite linear carbon chain.