We study (stationary) Laplacian transport by the Dirichlet-to-Neumann formalism. Our results concern a formal solution of the geometrically inverse problem for localisation and reconstruction of the form of absorbing domains. Here, we restrict our analysis to the one- and two-dimensional cases. We show that the last case can be studied by the conformal mapping technique. To illustrate this, we scrutinize the constant boundary conditions and analyze a numeric example.

We present a mathematical introduction to a widely used discrete tight-binding model for graphene. We also introduce the “Peierls substitution,” modelling the Hamiltonian of a 2d crystal in a perpendicular uniform magnetic field in this setting. We consider a discrete single-cone Hamiltonian closely related to the (double-cone) graphene Hamiltonian. Finally, we announce in this paper a result concerning an opening of gaps in the spectrum of this single-cone Hamiltonian, when the Peierls phase-factor arises from a weak, but non-zero, external magnetic field. Full proofs will be given elsewhere.

Let Ω ϲ R² be a domain having a compact boundary Σ which is Lipschitz and piecewise C⁴ smooth, and let ѵ denote the inward unit normal vector on Σ. We study the principal eigenvalue E(β) of the Laplacian in Ω with the Robin boundary conditions მ(f)/∂(ѵ)+β(f)= 0 on Σ, where β is a positive number. Assuming that Σ has no convex corners, we show the estimate E(β ) =-β²-γ_max +O(β^⅔) as β→+ꚙ ,where γ_max is the maximal curvature of the boundary.

We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by Maxwells equations. Both of the systems are controlled from the boundary. The inverse problems are to recover the manifold via the relevant measurements at the boundary (inverse data). We show that that the inverse data determine a C*-algebras, whose (topologized) spectra are identical to the manifold. By this, to recover the manifold is to determine a proper algebra from the inverse data, find its spectrum, and provide the spectrum with a Riemannian structure. This paper develops an algebraic version of the boundary control method (M.I.Belishev’1986), which is an approach to inverse problems based on their relations to control theory.

The local density of states of the carbon nanostructures can be calculated in different ways. Here, we present the Haydock recursion method which, using the Green’s function approach, transforms the given surface into a chain of equivalent sites. Then, using the continued fraction, we apply this procedure on the surface of the nanocylinders.

The classical capacity of quantum channels is the tight upper bound for the transmission rate of classical information. This is a quantum counterpart of the foundational notion of the channel capacity introduced by Shannon. Bosonic Gaussian quantum channels provide a good model for optical communications. In order to properly define the classical capacity for these quantum systems, an energy constraint at the channel input is necessary, as in the classical case. A further restriction to Gaussian input ensembles defines the Gaussian (classical) capacity, which can be studied analytically. It also provides a lower bound on the classical capacity and moreover, it is conjectured to coincide with the classical capacity. Therefore, the Gaussian capacity is a useful and important notion in quantum information theory. Recently, we have shown that the study of both the classical and Gaussian capacity of an arbitrary single-mode Gaussian quantum channel can be reduced to the study of a particular fiducial channel. In this work we consider the Gaussian capacity of the fiducial channel, discuss its additivity and analyze its dependence on the channel parameters. In addition, we extend previously obtained results on the optimal channel environment to the single-mode fiducial channel. In particular, we show that the optimal channel environment for the lossy, amplification, and phase-conjugating channels is given by a pure quantum state if its energy is constrained.

We present experimental and numerical results for a flux flow oscillator based on superconducting Josephson junctions. Our computationally efficient theoretical model takes into account Josephson self-coupling of the flux flow oscillator and is in a good agreement with our experimental results and previous studies.

Electronic transport in carbon nanoribbon is studied in a quantum graph model. A numerical method for current-voltage curve calculation is proposed. Various optimizations of a parallelization scheme are discussed. A parallel genetic algorithm to solve an inverse transport problem is invented.

The electrical properties of the granular silver films located on a surface of sapphire substrates are experimentally investigated during deposition and thermal annealing. The strong influence of surface-based silver atom diffusion on film formation is revealed, both during and after deposition. The effect of resistance switching in the films of the various thicknesses close to the percolation threshold, depending on the applied voltage is found and investigated. These sharp changes of resistance of 5–7 orders can be reversible or irreversible, depending on film thickness.

We study the existence of an infinite number of eigenvalues (the existence of Efimov’s effect) for a self-adjoint partial integral operators. We prove a theorem on the necessary and sufficient conditions for the existence of Efimov’s effect for the Fredholm type partial integral operators.

The electron scattering problem in the monolayer graphene with short range impurities is considered. The main novel element in the suggested model is the band asymmetry of the defect potential in the 2+1-dimensional Dirac equation. This asymmetry appears naturally if the defect violates the symmetry between sublattices. Our goal in the present paper is to take into account a local band asymmetry violation arising due to the defect presence. We analyze the effect of the electron scattering on the electronic transport parameters in monolayer graphene. The explicit exact formulae obtained for S-matrix for δ-shell potential allowed us to study the asymptotic behavior of such scattering data as scattering phases, transport cross section, the transport relaxation time and the conductivity for small values of the Fermi energy. The obtained results are in good agreement with experimental curves which show that the considered model is reasonable.

Spectral properties of a system are strongly associated with its geometry. The spectral problem for the Y-bent chain of weakly-coupled ball resonators is investigated. The Y-bent system can be described as a central ball linking three chains consisting of balls of the same radius. There is a δ-coupling condition with parameter α at every contact point. Specifically, it is assumed that the axis passing through the center of each ball lies in the same plane and the centers of balls that are the closest to the central ball form an equilateral triangle. The transfer-matrix approach and the theory of extensions are employed to solve the spectral problem for this system. It is shown that such system with a certain value of parameter α has at most one negative eigenvalue in the case of δ-coupling in contact points.

In this paper we investigate a quantum random number generator based on the splitting of a beam of laser emitted light. Statistics of random numbers that depend on a parameter characterizing the symmetry of the beam splitter is theoretically analyzed and simulated. Degree of deviation of the obtained distribution from the uniform random distribution is investigated on a basis of series of statistical tests.

In this paper we study the tunneling contact of carbon nanotubes with deep impurities and metal. The tunneling current in contact nanotube-metal was investigated. The dependence of current-voltage characteristic of such contact on the band gap of the impurity was analyzed. An area with negative differential conductivity was observed.

The paper deals with the problem of quantum particle storage in a nanolayered structures. The system of a few electrons interacting via a δ-potential is considered. The particles are placed into a two-dimensional deformed waveguide. From a mathematical point of view, the bound state of the system means that the corresponding Hamiltonian will have eigenvalues. To treat a multi-particle problem, the Hartree-Fock approach and the finite element method are used. Three different types of the perturbation are considered: deformation of the layer boundary, a small window in a wall between two layers and a bent layer. The systems of 2–10 particles with various total spins are studied. The dependence of the minimal deformation parameter, which keeps bound state on the number of particles, is given. Comparison of the storage efficiencies in those cases is made.

Current-voltage characteristics of tunnel contact between semiconducting (and conducting) carbon nanotubes (CNT) of various diameters and system of periodically located quantum dots (and also in contact to metal) was obtained using density of states (DOS) investigation. DOS has been calculated by means of the method of attached cylindrical waves. At certain parameters for quantum dots, the current-voltage characteristics observed testify to the presence of negative differential conductivity.

We consider Green’s function for layered system. We express it in terms of the well-known scalar s and p ones. For a single NIM layer in vacuum and with a single dispersive Lorentz form for equal electric and magnetic permeabilities ε(ω) and μ(ω), we obtain an explicit form for Green’s function. Also we find Green’s function for multilayered system and obtain recurrence relations for its coefficients.