Temperature Dependence of Microwave Photoresistance in 2D Electron Systems

We report on the temperature dependence of microwave-induced resistance oscillations in high-mobility two-dimensional electron systems. We find that the oscillation amplitude decays exponentially with increasing temperature, as $\exp(-\alpha T^2)$, where $\alpha$ scales with the inverse magnetic field. This observation indicates that the temperature dependence originates primarily from the modification of the single particle lifetime, which we attribute to electron-electron interaction effects.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Effect of an electric field on nucleation and growth of crystals

The effect of the electric field strength on nucleation and growth of the crystals of ammonium halides and alkali metal sulfates has been studied. The optimal electric field strength for NH[4]Cl and NH[4]Br crystals was found to be 15 kV/cm, and for NH[4]I, it equaled 10 kV/cm. No effect of the electric field strength on the crystal growth was found for alkali metal sulfates. This difference is analyzed in terms of the crystal growth thermodynamics. In case, when the electric field is small and the Gibbs energy is of a significant value, the influence of the electric field at the crystal growth is negligible. A method to estimate the critical radius of homogeneous nucleation of the crystal is suggested

Microwave Photoresistance in dc-driven 2D Systems at Cyclotron Resonance Subharmonics

We study microwave photoresistivity oscillations in a high mobility two-dimensional electron system subject to strong dc electric fields. We find that near the second subharmonic of the cyclotron resonance the frequency of the resistivity oscillations with dc electric field is twice the frequency of the oscillations at the cyclotron resonance, its harmonics, or in the absence of microwave radiation. This observation is discussed in terms of the microwave-induced sidebands in the density of states and the interplay between different scattering processes in the separated Landau level regime.Comment: 4 pages, 4 figure

Mathematical tools for computer-generated ornamental patterns

This article presents mathematical tools for computer-generated ornamental patterns, with a particular attention payed to Islamic patterns. The article shows how, starting from a photo or a sketch of an ornamental figure, the designer analyzes its structure and produces the analytical representation of the pattern. This analytical representation in turn is used to produce a drawing which is integrated into a computer-generated virtual scene. The mathematical tools for analysis of ornamental patterns consist of a subset of tools usually used in the mathematical theory of tilings such as planar symmetry groups and Cayley diagrams. A simple and intuitive step-by-step guide is provided

Spin-polarized supercurrents for spintronics: a review of current progress

During the past 15 years a new field has emerged, which combines superconductivity and spintronics, with the goal to pave a way for new types of devices for applications combining the virtues of both by offering the possibility of long-range spin-polarized supercurrents. Such supercurrents constitute a fruitful basis for the study of fundamental physics as they combine macroscopic quantum coherence with microscopic exchange interactions, spin selectivity, and spin transport. This report follows recent developments in the controlled creation of long-range equal-spin triplet supercurrents in ferromagnets and its contribution to spintronics. The mutual proximity-induced modification of order in superconductor-ferromagnet hybrid structures introduces in a natural way such evasive phenomena as triplet superconductivity, odd-frequency pairing, Fulde-Ferrell-Larkin-Ovchinnikov pairing, long-range equal-spin supercurrents, $\pi$-Josephson junctions, as well as long-range magnetic proximity effects. All these effects were rather exotic before 2000, when improvements in nanofabrication and materials control allowed for a new quality of hybrid structures. Guided by pioneering theoretical studies, experimental progress evolved rapidly, and since 2010 triplet supercurrents are routinely produced and observed. We have entered a new stage of studying new phases of matter previously out of our reach, and of merging the hitherto disparate fields of superconductivity and spintronics to a new research direction: super-spintronics.Comment: 95 pages, 23 Figures; published version with minor typos corrected and few references adde

Statistical Mechanics and the Physics of the Many-Particle Model Systems

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green's functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasiparticle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spin-fermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasiaverages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.Comment: 77 pages, 1 figure, Refs.37