Compacton matter waves are considered in Bose-Einstein condensates (BEC) and in binary BEC mixtures, trapped in deep optical lattices in the presence of strong and rapid periodic time modulations of the atomic scattering length, are considered. For this, we derive vector averaged discrete nonlinear Schr¨odinger equations (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system.

We discuss how the vertex boundary conditions for the dynamics of a quantum particle on a metric graph emerge when the dynamics is regarded as a limit of the dynamics in a tubular region around the graph. We give evidence for the fact that the boundary conditions are determined by the possible presence of a zero-energy resonance. Therefore, the boundary conditions depend on the shape of the fat graph near the vertex. We also give evidence, by studying the case of the half-line, for the fact that on the contrary, in general, adding on a graph a shrinking support potentials at the vertex either does not alter the boundary condition or does not produce a self-adjoint dynamics. Convergence, throughout, is meant in the sense of strongly resolvent convergence.

We address a linearized KdV equation on metric star graphs with one incoming finite bond and two outgoing semi-infinite bonds. Using the theory of potentials, we reduce the problem to systems of linear integral equations and show that they are uniquely solvable under conditions of the uniqueness theorem.

We treat the problem of the Green function for quantum graphs by focusing on such topologies as star and tree graphs. The exact Green function for the Schr¨odinger equation on primary star graphs is derived in the form of 3 × 3− matrix using the vertex boundary conditions providing continuity and current conservation. Extension of the approach for the derivation for the Green function on tree graph is presented. Possible practical applications of the obtained results are discussed.

The quantum dynamics of a hydrogen-like atom confined in one-dimensional box with oscillating walls is studied. The description of the system is reduced to a one-dimensional Schr¨odinger equation for Coulomb potential with time-dependent boundary conditions, which is solved numerically. Using the obtained solution, the average kinetic energy and binding energies are calculated as a function of time. It is found that both the average kinetic energy and the binding energies are periodic in time with the period depending on the wall’s oscillation parameters. The probability density is also analyzed as a function of time and coordinate.

The quantum dynamics of a delta-kicked driven particle in a star-shaped network is studied by obtaining an exact solution for the time-dependent Schr¨odinger equation within a single kicking period. The timedependence of the average kinetic energy and the Gaussian wave packet evolution are analyzed.

Second harmonic generation in 2D nonlinear photonic crystals based on rectangular symmetry with rectangular motifs has been analyzed theoretically. An approximate solution of the spectral response for the second harmonic generation in any designed 2D nonlinear photonic crystal is obtained within the un-depleted pump approximation. Rapid calculation of the temporal profile of multidirectional second harmonic pulse in such nonlinear lattices has been also shown.

An adiabatic change of parameters along a closed path may interchange the (quasi-)eigenenergies and eigenspaces of a closed quantum system. Such discrepancies, induced by adiabatic cycles are referred to as the exotic quantum holonomy, which is an extension of the geometric phase. \Small" adiabatic cycles induce no change on eigenspaces, whereas some \large" adiabatic cycles interchange eigenspaces. We explain the topological formulation for the eigenspace anholonomy, where the homotopy equivalence precisely distinguishes the larger cycles from smaller ones. An application to two level systems is explained. We also examine the cycles that involve the adiabatic evolution across an exact crossing, and the diabatic evolution across an avoided crossing. The latter is a nonadiabatic example of the exotic quantum holonomy.

We study the solution for a system of reaction-diffusion equations with double nonlinearity in the presence of a source. A self-similar approach is used for the treatment of qualitative properties of a nonlinear reactiondiffusion system. It is shown that there exist some parameter values for which the effect of finite velocity of perturbation of distribution (FSPD), localization of solution, onside localization can occur. The problem for choosing the appropriate initial approximation for the iteration process used in numerical analysis is solved.

The most intriguing observation of cuprate experiments is most likely the metal-insulator-crossover (MIC), seen in the underdome region of the temperature-doping phase diagram for copper-oxides under a strong magnetic field, when superconductivity is suppressed. This MIC, which results in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, nonlinear entropy, insulating ground state, nematicity- and stripe-phases and Fermi pockets, reveals the nonconventional dielectric property of the pseudogap-normal phase. Since conventional superconductivity appears from a conducting normal phase, the understanding of how superconductivity arises from an insulating state becomes a fundamental problem and thus the keystone for all of cuprate physics. Recently, in interpreting the physics of visualization in scanning tunneling microscopy (STM) real space nanoregions (NRs), which exhibit an energy gap, we have succeeded in understanding that the minimum size for these NRs provides pseudogap and superconductivity pairs, which are single bosons. In this work, we discuss the intra-particle magnetic spin and charge fluctuations of these bosons, observed recently in hidden magnetic order and STM experiments. We find that all the mentioned MIC phenomena can be obtained in the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of sample percolating NRs of single fermions into those of single bosons.

This work presents a model for the degradation mechanism of organic{inorganic hybrid photovoltaic solar cells based on perovskites. The cross section for formation of Frenkel pairs in the sublattice of iodine is obtained. The channels for its annealing are found. Special attention is paid to the polaron states. It is shown that the stationary number of defects non-monotonically depends on the intensity of solar radiation. This allows one to analyze the properties of the radiation resistance of a device to ionizing radiation.

We describe the features of the conversion of electrical current into light in light diodes based on an organic matrix containing semiconductor quantum dots. It is shown that the relaxation channels of nonequilibrium electron-hole plasma injected into the quantum dot of the current density through the device. The conversion efficiency increases significantly with a decrease in the radius of the quantum dot.

In this work the dependence between the position of single charge trapped in an oxide layer or at SiO2 { Si3N4 interface and the concentration distribution of charge carriers on a semiconductor substrate surface of the nanometer n-channel Metal-Nitride-Oxide-Semiconductor Field Effect Transistor (MNOSFET) and p-channel MNOSFET with n+ drain area is studied. It is shown that the lateral capacitances of nanometer MNOSFET depend on the position of single charge in oxide or at interface. This dependence allows one to estimate the position of trapped charges along the channel of transistor.

CoOOH nanolayers were first prepared by the successive ionic layer deposition (SILD) method using aqueous Co(OAc)2 and K2S2O8 solutions. The obtained nanolayers were investigated by SEM, EDX, XRD, FTIR spectroscopy and electrochemical techniques. SEM images showed that the layers formed by nanosheets of size approximately 80-100 nm which had a hexagonal crystal structure. Electrochemical study of nickel foam electrodes modified by CoOOH layer prepared by 50 SILD cycles demonstrates that specific capacitance of the film is 1520 F/g at current density 1 A/g. Repeated cycling for 1000 charge-discharge cycles demonstrates 2% capacitance fade, so such electrodes may be used as pseudocapacitor electrodes.

Here, we show successful filling of 1.4 nm single-walled carbon nanotubes (SWNT) with PbTe nanocrystals. The structure of one-dimensional PbTe in SWNT was determined using high-resolution transmission electron microscopy (HRTEM). The electronic structure of composites was studied by optical absorbance and Raman spectroscopies indicating no noticeable interaction of encapsulated PbTe with SWNT wall. Experimental data are supported by ab-initio calculations, showing non-zero density of states at the Fermi level of PbTe@SWNT(10,10) provided by both SWNT and PbTe states and thus metallic conductivity of the composite.

The phenomenological parameters of the Hamiltonian for the photons produced in earlier studies [4] are associated with the parameters of the deformed optical fiber (OF). This Hamiltonian is necessary for the correct description of the propagation of photons through the quantum channel in a quantum communication protocols. Models of a compressing strain of the OF profile and a twisting deformation are considered. As a consequence, the phenomenological parameters of the Hamiltonian expressed in terms of such strains characteristics, as a relative compression of the profile, OF radius, the orientation angle of the deformed profile, rotation angle per unit length, elasto-optical tensor, and refraction coefficient.

Yttrium orthoferrite nanocrystallites with hexagonal and orthorhombic structures were obtained directly by the glycine-nitrate synthesis. The nanocrystallites have plate-like morphology and are strongly agglomerated in highlyporous structures, as was shown by the TEM investigation. The influences of the synthesis conditions on the yttrium orthoferrite crystallization, its nanocrystallite size and morphology are discussed.

A study of oxygen atoms’ interactions on a GaAs (001) structure surface shows that these atoms are getting adsorbed onto the surface, form an oxide layer, and over time its thickness increases. This oxide layer hinders the injection of electrons and the holes from the metal layer to the semiconductor, thus affecting the photoelectroluminescence and the work of Metal-oxide-semiconductor diodes. These studies also examine the growth rate of oxide layers on the surface of the structure with different deposition degrees (400 ◦C, 630 ◦C) of cover layers and the extent of the oxygen atoms’ penetration into the structure.

This paper presents the results of Monte Carlo (MC) simulation for paramagnetic, ferromagnetic and anti-ferromagnetic transitions in 2D thin films. The spin coarsening which lowers energy brings order at the cost of lowering entropy in the presence of an external magnetic field, which in turn, may increase the free energy at relatively higher temperatures because of spin mixing. There is a competition between energy of the system and entropy in conserved and non-conserved binary mixtures in the presence of an external magnetic field. The simulation is done on a lattice of size 100×100 using Metropolis algorithm with periodic boundary conditions. All data are sampled for 20 K MC cycles after a regular interval of 100 MC cycles. The paramagnetic case with spin coupling coefficient and the ferromagnetic and anti-ferromagnetic cases with j"(AB)j = 0:0J0, 0:25J0, 0:50J0, 0:75J0 & 1:0J0 (keeping j"(AA)j = j"(BB)j = 1:0J0) (Here J0 = 1:0 unit of energy) are studied at temperatures kT = 0:25J0, 0:50J0, 0:75J0, 1:0J0, 1:25J0, 1:5J0, 1:75J0, & 2:0J0 in presence of varying external magnetic field strengths in order to observe the organizational behavior of spins and the interplay between the free energy and entropy. The induced magnetization and the magnetic susceptibilities are found to be in qualitative agreement with the theory. The paramagnetic to ferromagnetic transition has been observed and explored at high T values. The spin correlation function plotted helps to reveal the spin transport properties of the systems. The spontaneous ferromagnetic transition temperatures for "(AB) = 1:0J0, 0:75J0 & 0:50J0 are observed as kBT = 0:44J0, 0:39J0 & 0:33J0 (i.e. nearly 96 % magnetizations are observed at these temperatures) respectively at B = 0:0J0=µ (i.e. absence of any external magnetic field). This is in quantitative agreement with theory. The spin correlation function diverges at these transition temperatures, which can be understood as the theoretical evidence supporting the observation of spontaneous magnetization. The ferromagnetic to paramagnetic transitions are not very sharp but the range of the spin-spin interaction can be said to decay gradually. Even at higher temperature as kT = 2:0J0, the opposite spin pair correlation function supports formation of tiny domains with spin transport from one domain to another, whereas for lower temperatures below kT = 1:0J0, the presence of majority +1=2 spins diminish the effect. Tiny domain walls have lower energy surrounded by opposite spins and seem to be energetically preferred. This quasi nature of spin-spin interaction with temperature is also supported by the corresponding ensemble entropy averages.