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## Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene

We study tunneling of charge carriers in single- and bilayer graphene. We propose an explanation for nonzero “magic angles” with 100% transmission for the case of symmetric potential barrier, as well as for their almost-survival for slightly asymmetric barrier in the bilayer graphene known previously from numerical simulations. Most importantly, we demonstrate that these magic angles are *not* protected in the case of bilayer and give an explicit example of a barrier with very small electron transmission probability for *any* angles. This means that one can lock charge carriers by a *p-n-p* (or *n-p-n*) junction *without* opening energy gap. This creates new opportunities for the construction of graphene transistors.

The optical properties of graphene-based structures are discissed. The universal optical absorption in graphene is reviewed. The photonic band structure and transmission of graphene-based photonic crystals are considered. The spectra of plasmon and magnetoplasmon excitations in graphene layers and grapehene nanoribbons (GNR) are analyzed. The localization of the electromagnetic waves in the photonic crystals with defects, which play a role of waveguide, is studied. Properties of plasmons and magnetoplasmons in graphene layers and GNR are reviewed. The surface plasmon amplification by stimulated emission of radiation with the net amplification of surface plasmons in the doped GNR is described. The minimal population inversion per unit area needed for the net amplification of plasmons in a doped GNR is reported. The various applications of graphene for photonics and optoelectronics are reviewed. The tunability of photonic and plasmonic properties of various graphene structures by doping achieved by applying the gate voltage is discussed.

Graphene synthesis technology on substrates is promising, as is compatible with existing CMOS-technology. Knowledge about how to affect the substrate of choice for structural and electronic properties of graphene is important and opens up new opportunities in targeted influence on the properties of this unique material. Specialized measuring system was established to measure the galvanomagnetic characteristics of substrates multigraphene. Its structure and the measurement results are presented in the paper. For surface resistivity measurements we obtained samples were higher than that of natural graphite, but much lower than for samples of colloidal suspensions.

The behavior of the TE and TM electromagnetic waves in graphene at the interface between two semi-infinite dielectric media is studied. The dramatic influence on the TE waves propagation even at very small changes in the optical contrast between the two dielectric media is predicted. Frequencies of the TE waves are found to lie only in the window determined by the contrast. We consider this effect in connection with the design of graphene-based optical gas sensor. Near the frequency, where the imaginary part of the conductivity of graphene becomes zero, ultrahigh refractive index sensitivity and very low detection limit are revealed. The considered graphene-based optical gas sensor outperforms characteristics of modern volume refractive index sensors by several orders of magnitude.

We discuss some well-known facts about Clifford algebras: matrix representations, Cartan’s periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in <span data-mathml="nn dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the method of averaging in Clifford algebras, the notion of quaternion type of Clifford algebra elements, the classification of Lie subalgebras of specific type in Clifford algebra, etc.

We show that the Foldy-Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of the Dirac equation but also in other problems.

A novel type of spaser with the net amplification of surface plasmons (SPs) in a doped graphene nanoribbon is proposed. The plasmons in the THz region can be generated in a doped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon, is obtained. The dependence of the minimal population inversion on the surface plasmon wave vector, graphene nanoribbon width, doping, and damping parameters necessary for the amplification of surface plasmons in the armchair graphene nanoribbon is studied.

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.

By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.

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.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

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.