Atomic States Entanglement in Carbon Nanotubes

The entanglement of two atoms (ions) doped into a carbon nanotube has been investigated theoretically. Based on the photon Green function formalism for quantizing electromagnetic field in the presence of carbon nanotubes, small-diameter metallic nanotubes are shown to result in a high degree of the two-qubit atomic entanglement for long times due to the strong atom-field coupling.Comment: 4 pages, 2 figure

Heterogeneous product and process innovations for a multi-product monopolist under finite life-cycles of production technologies.

Current paper analyses the influence of the length of production technologies life-cycles on the relative intensity of investments of a multi-product monopolist into different types of innovations. This monopolist is developing new versions of the basic product continuously and simultaneously invests into the production technologies of all these new products. In the paper the finite character of these products' life-cycles is assumed. These finite life-cycles are treated for the purposes of the paper as patents which are granted to the monopolist for the production and upgrading of every new product he/she introduces into the market. It is demonstrated that under the condition of finite-time life-cycles of new products the monopolist prefers to invest into process innovations for already introduced products rather than introducing the new ones in relative measure. It is argued, that this is not the case under infinite life-cycles for all these products where the monopolist invests relatively the same amounts into both types of innovations

The Numerical Solution in the Sense of Prager&Synge

The solution in sense of Prager&Synge is the alternative to the commonly used notion of the numerical solution, which is considered as a limit of grid functions at mesh refinement. Prager&Synge solution is defined as a hypersphere containing the projection of the true solution of the system of partial differentiation equations (PDE) onto the computational grid and does not use any asymptotics. In the original variant it is determined using orthogonal properties specific for certain equations. In the proposed variant, the center and radius of the hypersphere is estimated using the ensemble of numerical solutions obtained by independent algorithms. This approach may be easily expanded for solutions of an arbitrary system of partial differentiation equations that significantly expands the domain of its applicability. Several options for the computation of the Prager&Synge solution are considered and compared herein. The first one is based on the search for the orthogonal truncation errors and their transformation. The second is based on the orthogonalization of approximation errors obtained using the defect correction method and applies a superposition of numerical solutions. These options are intrusive. In third option (nonintrusive) the information regarding orthogonality of errors, which is crucial for the Prager&Synge approach method, is replaced by information that stems from the properties of the ensemble of numerical solutions, obtained by independent numerical algorithms. The values of the angle between the truncation errors on such ensemble or the distances between elements of the ensemble may be used to replace the orthogonality. The variant based on the width of the ensemble of independent numerical solutions does not require any additional a priori information and is the approximate nonintrusive version of the method based on the orthogonalization of approximation errors.Comment: 22 pages, 8 figure

Doubly differential cross sections for ionization of lithium atom by protons and O8+^{8+} ions

We consider single ionization of lithium atom in collisions with $p$ and O$^{8+}$ projectiles. Doubly differential cross sections for ionization are calculated within a relativistic non-perturbative approach. Comparisons with the recent measurements and theoretical predictions are made.Comment: Submitted to the Topical Issue of Eur. Phys. J. D based on the contributions reported on the International Conference on Many Particle Spectroscopy of Atoms, Molecules, Clusters and Surfaces (MPS 2018), Budapest, Hungary, 21-24 August 201