Canonical description of ideal magnetohydrodynamic flows and integrals of motion

In the framework of the variational principle the canonical variables describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with spatially varying entropy and nonzero values of all topological invariants) are introduced. The corresponding complete velocity representation enables us not only to describe the general type flows in terms of single-valued functions, but also to solve the intriguing problem of the ``missing'' MHD integrals of motion. The set of hitherto known MHD local invariants and integrals of motion appears to be incomplete: for the vanishing magnetic field it does not reduce to the set of the conventional hydrodynamic invariants. And if the MHD analogs of the vorticity and helicity were discussed earlier for the particular cases, the analog of Ertel invariant has been so far unknown. It is found that on the basis of the new invariants introduced a wide set of high-order invariants can be constructed. The new invariants are relevant both for the deeper insight into the problem of the topological structure of the MHD flows as a whole and for the examination of the stability problems. The additional advantage of the proposed approach is that it enables one to deal with discontinuous flows, including all types of possible breaks.Comment: 16 page

Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy

The manipulation of light by conventional optical components such as a lenses, prisms and wave plates involves engineering of the wavefront as it propagates through an optically-thick medium. A new class of ultra-flat optical components with high functionality can be designed by introducing abrupt phase shifts into the optical path, utilizing the resonant response of arrays of scatters with deeply-subwavelength thickness. As an application of this concept, we report a theoretical and experimental study of birefringent arrays of two-dimensional (V- and Y-shaped) optical antennas which support two orthogonal charge-oscillation modes and serve as broadband, anisotropic optical elements that can be used to locally tailor the amplitude, phase, and polarization of light. The degree of optical anisotropy can be designed by controlling the interference between the light scattered by the antenna modes; in particular, we observe a striking effect in which the anisotropy disappears as a result of destructive interference. These properties are captured by a simple, physical model in which the antenna modes are treated as independent, orthogonally-oriented harmonic oscillators

Quasi-long-range order in nematics confined in random porous media

We study the effect of random porous matrices on the ordering in nematic liquid crystals. The randomness destroys orientational lang-range order and drives the liquid crystal into a glass state. We predict two glass phases one of which possesses quasi-long-range order. In this state the correlation length is infinite and the correlation function of the order parameter obeys a power dependence on the distance. The small-angle light-scattering amplitude diverges but slower than in the bulk nematic. In the uniaxially strained porous matrices two new phases emerge. One type of strain induces an anisotropic quasi-long-range-ordered state while the other stabilizes nematic long-range order.Comment: 4 pages, Revte

Aberration-free ultra-thin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces

The concept of optical phase discontinuities is applied to the design and demonstration of aberration-free planar lenses and axicons, comprising a phased array of ultrathin subwavelength spaced optical antennas. The lenses and axicons consist of radial distributions of V-shaped nanoantennas that generate respectively spherical wavefronts and non-diffracting Bessel beams at telecom wavelengths. Simulations are also presented to show that our aberration-free designs are applicable to high numerical aperture lenses such as flat microscope objectives

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is therefore realized either along one trajectory or along two equivalent paths. Zero point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multi-stability and tunneling phenomena.Comment: 11 pages, 8 eps figures, Revtex-

Long Wavelength Anomalous Diffusion Mode in the 2D XY Dipole Magnet

In 2D XY ferromagnet the dipole force induces a strong interaction between spin-waves in the long-wavelength limit. The major effect of this interaction is the transformation of a propagating spin-wave into a diffusion mode. We study the anomalous dynamics of such diffusion modes. We find that the Janssen-De Dominics functional, which governs this dynamics, approaches the non-Gaussian fixed-point. A spin-wave propagates by an anomalous anisotropic diffusion with the dispersion relation: $i\omega{\sim}k_{y}^{\Delta_y}$ and $i\omega{\sim}k_{x}^{\Delta_x}$, where ${\Delta_y}=47/27$ and ${\Delta_x}=47/36$. The low-frequency response to the external magnetic field is found.Comment: 34 pages, RevTeX, 2 .ps figures, the third figure is available upon reques

Soft Spectrum in Yukawa-Gauge Mediation

We introduce a model independent parametrization for a subclass of gauge mediated theories, which we refer to as Yukawa-gauge mediation. Within this formalism we study the resulting soft masses in the visible spectrum. We find general expressions for the gaugino and scalar masses. Under generic conditions, the gaugino mass is screened, vanishing at first order in the SUSY breaking scale.Comment: 22 pages, 4 figures; v2: minor corrections, published versio

Flavor Mediation Delivers Natural SUSY

If supersymmetry (SUSY) solves the hierarchy problem, then naturalness considerations coupled with recent LHC bounds require non-trivial superpartner flavor structures. Such "Natural SUSY" models exhibit a large mass hierarchy between scalars of the third and first two generations as well as degeneracy (or alignment) among the first two generations. In this work, we show how this specific beyond the standard model (SM) flavor structure can be tied directly to SM flavor via "Flavor Mediation". The SM contains an anomaly-free SU(3) flavor symmetry, broken only by Yukawa couplings. By gauging this flavor symmetry in addition to SM gauge symmetries, we can mediate SUSY breaking via (Higgsed) gauge mediation. This automatically delivers a natural SUSY spectrum. Third-generation scalar masses are suppressed due to the dominant breaking of the flavor gauge symmetry in the top direction. More subtly, the first-two-generation scalars remain highly degenerate due to a custodial U(2) symmetry, where the SU(2) factor arises because SU(3) is rank two. This custodial symmetry is broken only at order (m_c/m_t)^2. SUSY gauge coupling unification predictions are preserved, since no new charged matter is introduced, the SM gauge structure is unaltered, and the flavor symmetry treats all matter multiplets equally. Moreover, the uniqueness of the anomaly-free SU(3) flavor group makes possible a number of concrete predictions for the superpartner spectrum.Comment: 17 pages, 7 figures, 2 tables. v2 references added, minor changes to flavor constraints and a little discussion adde

Black Holes in Ho\v{r}ava Gravity with Higher Derivative Magnetic Terms

We consider Horava gravity coupled to Maxwell and higher derivative magnetic terms. We construct static spherically symmetric black hole solutions in the low-energy approximation. We calculate the horizon locations and temperatures in the near-extremal limit, for asymptotically flat and (anti-)de Sitter spaces. We also construct a detailed balanced version of the theory, for which we find projectable and non-projectable, non-perturbative solutions.Comment: 17 pages. v2: Up to date with published version; some minor remarks and more reference