### Article

## Topological Phase and Half-Integer Orbital Angular Momenta in Circular Quantum Dots

We show that there exists a non-trivial topological phase in circular two-dimensional quantum dots with an odd number of electrons. The possible non-zero value of this phase is explained by axial symmetry of two-dimensional quantum systems. The particular value of this phase (1995). Hence, these data may be considered as the first experimental evidence for the existence of topological phase leading to half-integer quantization of the orbital angular momentum in circular quantum dots with an odd number of electrons.

We report on broad-area lasers, mode-locked lasers (MLLs), and superluminescent light-emitting diodes (SLDs) based on a recently developed novel type of nanostructures that we refer to as quantum well-dots (QWDs). The QWDs are intermediate in properties between quantum wells and quantum dots and combine some useful properties of both. 1.08 μm InGaAs/GaAs QWDs broad area edge-emitting lasers based on coupled large optical cavity waveguides show high internal quantum efficiency of 92%, low internal loss of 0.9 cm-1 and material gain of ~1.1∙104 cm-1 per one QWD layer. CW output power of 14.2 W is demonstrated at room temperature. Superluminescent light-emitting diodes with one QWD layer in the active region exhibit stimulated emission spectra centered at 1050 nm with the maximal full width at half maximum of 36 nm and the output power of 17 mW. First results on mode-locked operation in QWD lasers are also presented. 2 mm long two-section devices demonstrate the pulse repetition rate of 19.3 GHz and the pulse duration of 3.5 ps. The width of the radio frequency spectrum is 0.2 MHz.

We analyzed the localized charge dynamics in the system of interacting single-level quantum dots (QDs) coupled to the continuous spectrum states in the presence of Coulomb interaction between electrons within the dots. Different dots geometry and initial charge configurations were considered. The analysis was performed by means of Heisenberg equations for localized electrons pair correlators. We revealed that charge trapping takes place for a wide range of system parameters and we suggested the QDs geometry for experimental observations of this phenomenon. We demonstrated significant suppression of Coulomb correlations with the increasing of QDs number. We found the appearance of several time scales with the strongly different relaxation rates for a wide range of the Coulomb interaction values.

We demonstrated that electron-phonon interaction leads to the increasing of localized charge relaxation rate. We also found that several time scales with different relaxation rates appear in the system in the case of non-resonant tunneling between the dots. We revealed the formation of oscillations in the filling numbers time evolution caused by the emission and adsorption processes of phonons.

The problems of creation of a low intensity optical radiation signal standard sources based on the nanosized apertures and semiconductor quantum dots are considered. The use of technology of the focused ionic beam technology for isolation of a single quantum dot is offered suggested.

Quantum dot based monolithic edge-emitting semiconductor lasers at 1.25 m are ideal sources for the generation of broad optical frequency combs for optical communication applications. In this work, InAs/InGaAs quantum dot lasers with dierent total laser length to absorber length ratio and with dierent p-doping concentrations in the GaAs barrier sections are investigated experimentally in dependence on the gain injection current and absorber reverse bias voltage. A smaller mode-locking area is found for the p-doped device in dependence on the laser biasing conditions. For the undoped active region 1.3 ps short pulse widths at a pulse repetition rate of 20 GHz with a pulse-to-pulse timing jitter of 111 fs are reported for an absorber section length of 12% to the total cavity length. For an undoped and p-doped device short pulse emission between 2.5 ps and 5.5 ps is attained and a shorter absorber section length of 8% or 5%.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.