Elastic light scattering by semiconductor quantum dots of arbitrary shape

Elastic light scattering by low-dimensional quantum objects without a change in the frequency is theoretically investigated in terms of the quantum perturbation theory. The differential cross section of resonance light scattering from any excitons in any quantum dots is calculated. It is demonstrated that, when the light wavelengths considerably exceed the quantum-dot size, the polarization and angular distribution of the scattered light do not depend on the shape, the size, or the configuration of quantum dots. In this case, the total light scattering cross section is independent of the quantum-dot size. If the radiative damping of an exciton exceeds the nonradiative damping, the total light scattering cross section at resonance is of the order of the light wavelength squared. The radiative damping associated with the long-range exchange interaction between electrons and holes is calculated for any excitons and any quantum dots.     

Asymptotic observers for bilinear systems with vector output

We construct asymptotic observers for bilinear systems with vector output. Various cases in which the rank of the bilinearity matrix drops are considered.     

Some comments on stability of infinite-dimensional systems

The article proposes an infinite-dimensional generalization of the Lyapunov second method for stability analysis of dynamical systems. Translated from Nelineinaya Dinamika i Upravlenie, pp. 15–21, 1999.     

On the reactivity of isoindolo[2,1-a]quinazoline-5-ones

Base- and acid-catalyzed nucleophilic addition of 11H-isoindolo[2,1-a]quinazoline-5-one to aromatic aldehydes and maleimides was investigated. The aldol adducts and condensation products were obtained stereoselectively. Main diastereomers of the Michael adducts were isolated in 74-89% yield, and converted by N-methylation to new stable α-substituted isoindole derivatives, for which 6-methylisoindolo[2,1-a]]quinazoline-5-one stands as the unsubstituted reference. The stability of the latter was monitored in moist aerated CDCl₃ solution, and one of the oxidative hydrolysis product was characterized by X-ray diffraction analysis as the corresponding N-arylphthalimide. The reactivity of the unsubstituted 6-methylisoindolo[2,1-a]]quinazoline-5-one was also investigated with acetylenic Michael acceptors. Fully conjugated isoindole derivatives possessing an original pull-push-pull structure were obtained. The conformations and molecular orbitals of the dibenzoylacetylene adduct were studied at the DFT level of theory. Its static quadratic hyperpolarizabilty β₀ was also calculated at the ZINDO level.     

Spectrum of an electron spin coupled to an unpolarized bath of nuclear spins

The main source of decoherence for an electron spin confined to a quantum dot is the hyperfine interaction with nuclear spins. To analyze this process theoretically we diagonalize the central spin Hamiltonian in the high magnetic B-field limit. Then we project the eigenstates onto an unpolarized state of the nuclear bath and find that the resulting density of states has Gaussian tails. The level spacing of the nuclear sublevels is exponentially small in the middle of each of the two electron Zeeman levels but increases superexponentially away from the center. This suggests to select states from the wings of the distribution when the system is projected on a single eigenstate by a measurement to reduce the noise of the nuclear spin bath. This theory is valid when the external magnetic field is larger than a typical Overhauser field at high nuclear spin temperature.     

Vortex lattice matching effects in a washboard pinning potential induced by Co nanostripe arrays

An advanced mask-less nanofabrication technique, focused electron beam-induced deposition (FEBID), has been employed on epitaxial Nb thin films to prepare ferromagnetic decorations in the form of an array of Co stripes. These substantially modify the non-patterned films’ superconducting properties, providing a washboard-like pinning potential landscape for the vortex motion. At small magnetic fields B ? 0.1 T, vortex lattice matching effects have been investigated by magneto-transport measurements. Step-like drops in the field dependencies of the films resistivity ρ(B) have been observed in particular for the vortex motion perpendicular to the Co stripes. The field values, corresponding to the middle points of these drops in ρ(B), meet the vortex lattice parameter matching the pinning structure’s period. These disagree with the results of Jaque et al. (2002) [11], who observed matching effects corresponding to the stripe width in Nb films grown on periodically distributed submicrometric lines of Ni.     

Desynchronization transitions in nonlinearly coupled phase oscillators

We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous state to partial synchrony is performed. We demonstrate that for small ensembles it is typically mediated by stable cluster states, that disappear with creation of heteroclinic cycles, while for a larger number of oscillators a direct transition from full synchrony to a periodic or a quasiperiodic regime occurs.     

Gold film-terminated 3-dimensional photonic crystals

Hybrid metal-dielectric photonic crystals assembled from an opal film coated by a gold film are designed in order to realize optical spectra that emanate from mixing Bloch modes in the opal and surface plasmon polaritons in corrugated gold films. The photonic crystal provides a spatial template for the gold film profile and modifies the electromagnetic vacuum in the vicinity to the gold layer. Reflectance spectroscopy was applied to deconvolute the plasmonic and photonic bandgap components in the optical response of hybrid crystals as opposite to their mixed appearance in the transmission spectra.