Vol 104, No 1 (2016)

We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation R = [2, 2] for quantum groups U_q(sl_N). Most of them have sizes 2, 3, and 4 and are fully described by the eigenvalue hypothesis. Of two 6 × 6 matrices, one is also described in this way, but the other one corresponds to the case of degenerate eigenvalues and is evaluated by the highest weight method. Together with the much harder calculation for R = [3, 1] and with the new method to extract exclusive matrices J and \(\overline J\) from the inclusive ones, this completes the story of Racah matrices for |R| ≤ 4 and allows one to calculate and investigate the corresponding colored HOMFLY polynomials for arbitrary 3-strand and arborescent knots.

We study the influence of the meson cloud of the nucleon on predictions of the Monte Carlo Glauber model for the charged particle multiplicity density at mid-rapidity in AA collisions. We find that for central AA collisions the meson cloud can increase the multiplicity density by ~16–18%. The meson–baryon Fock component reduces the required fraction of the binary collisions by a factor of ~2 for Au + Au collisions at \(\sqrt s = 0.2TeV\) and ~1.5 for Pb + Pb collisions at \(\sqrt s = 2.78TeV\).

At large accelerators, bent crystals are employed to deflect weakly divergent proton beams at the stages of extraction and collimation. We demonstrate that a divergent particle beam may be efficiently deflected using a crystal with a focusing edge. A proton beam with divergence near 1 mrad, which exceeds the Lindhard angle by a factor of 30, has been experimentally deflected by 1.8 mrad with efficiency near 15%. The proposed focusing crystal may serve as an element of a novel optical system for secondary-particle beams in the TeV energy region.

We experimentally investigate transport through the side junction between a niobium superconductor and the mesa edge of a two-dimensional system, realized in an InAs/GaSb double quantum well with band inversion. We demonstrate, that different transport regimes can be achieved by variation of the mesa step. We observe anomalous behavior of Andreev reflection within a finite low-bias interval, which is invariant for both transport regimes. We connect this behavior with the transition from retro-(at low biases) to specular (at high ones) Andreev reflection channels in an InAs/GaSb double quantum well with band inversion.

The spatial variation of the orbital part of the order parameter of ³He-A in an aerogel has been represented as random walk of a unit vector l(r) over a sphere under the action of random anisotropy created by the system of strands of the aerogel. The statistical properties of the resulting random texture have been studied. For distances at which the variation of l is much smaller than its magnitude, the average square <δl²> of variation of l has been expressed in terms of the correlation function of the component of the random anisotropy tensor. Under simplifying assumptions on the structure of this correlation function, an analytical dependence of <δl²> on r has been obtained for isotropic and axially anisotropic aerogels. The average values of the squares of the projections of l on the axes of anisotropy for an anisotropic aerogel have been represented in terms of the parameters of the aerogel. The characteristic scale at which the long-range order is broken, as well as the magnitude of global anisotropy sufficient for the recovery of the long-range order, has been numerically estimated within a simple model. The values obtained have been compared to other estimates.

The properties of plasma and magnetoplasma excitations in free-hanging graphene have been studied for the first time by Raman scattering. In addition to single-particle excitations associated with transitions between empty Landau levels of electrons and holes, collective plasma and magnetoplasma excitations in the system of electrons (and holes) of various densities have been discovered for the first time. Hybridization of plasma and cyclotron modes corresponding to the Kohn law has been shown to occur in the limit of high filling factors, which allows measuring directly the plasma and cyclotron energies. The dependence of the electron and hole velocities on their density has been investigated via the magnetic-field dependence of the cyclotron energy in free-hanging graphene. The effect of strong renormalization of the electron and hole dispersion relations seen as an increase in the velocity (by 40–50%) with a decrease in the charge-carrier density to 10¹¹ cm^–2 has been discovered. The charge-carrier density dependences of the widths of magnetoplasma resonances in free-hanging graphene and graphene lying on a silicon dioxide surface have been measured and shown to be at least 3.5 and 14.8 meV, respectively.

It is found that the resistivity of EuBaCo₂O_5.5 depends not only on the magnitude of an applied magnetic field but also on its sign. This phenomenon is new for cobalt and manganese oxides. The symmetric or shifted hysteresis loops (depending on the cooling method) for the resistivity correspond to similar loops for the magnetization. The angular dependence of the resistivity is described by the relation Δρ ~ sinθ, where the angle θ = 0 corresponds to the direction of magnetization, at which the sample has been cooled. The results are interpreted in terms of the exchange interaction between the ferromagnetic (FM) and antiferromagnetic (AFM) phases. At the cyclic variation of temperature or magnetic field, the resistivity of EuBaCo₂O_5.5 increases and does not return to the initial state. The metastable state of EuBaCo₂O_5.5 is related to the kinetic phenomena accompanying the first order FM–AFM phase transition.

A new hyperbolic metamaterial based on a modified semiconductor Bragg mirror structure with embedded periodically arranged quantum wells is proposed. It is shown that exciton polaritons in this material feature hyperbolic dispersion in the vicinity of the second photonic band gap. Exciton–photon interaction brings about resonant nonlinearity leading to the emergence of nontrivial topological polaritonic states. The formation of spatially localized breather-type structures (oscillons) representing kink-shaped solutions of the effective Ginzburg–Landau–Higgs equation slightly oscillating along one spatial direction is predicted.