Integrability of higher pentagram maps

We define higher pentagram maps on polygons in $\mathbb{P }^d$ for any dimension $d$ , which extend R. Schwartz’s definition of the 2D pentagram map. We prove their integrability by presenting Lax representations with a spectral parameter for scale invariant maps. The corresponding continuous limit of the pentagram map in dimension $d$ is shown to be the $(2,d+1)$ -equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. We also study in detail the 3D case, where we prove integrability for both closed and twisted polygons and describe the spectral curve, first integrals, the corresponding tori and the motion along them, as well as an invariant symplectic structure.     

Progress in the area of new energy-efficient basic elements for superconducting electronics

This review is devoted to a discussion of the prospects for solving the problem of a low degree of integration of the traditional elements for promising (due to the high performance and extremely low energy dissipation) superconducting digital electronics. We define three main directions on the path to compact multi-element Josephson electronic systems: (1) reduction of the Josephson junction to submicron size, (2) decrease of the area of standard logic cells, and (3) fabrication of a compact and rapid Josephson memory. We present the physical foundations of Josephson elements in order to show the fundamental constraints on establishing standard submicron tunnel contacts and compact logic cells/memory elements. This survey clearly demonstrates the essence of breakthrough technological solutions to create ultrasmall heterostructures with desired settings, reduce and optimize logic cells, and create memory unit cells based on Josephson junctions with magnetic layers.     

Depolarization of the electromagnetic field in a locally inhomogeneous earth-ionosphere waveguide

This paper presents a further development of the numerical-analytical method for the solution of three-dimensional problems in the theory of radio wave propagation. We consider a vector problem of the electromagnetic field of a vertical electric dipole in a plane Earth-ionosphere waveguide with a local large-scale irregularity on the anisotropic ionosphere wall. The possibility of lowering (elevating) of the local region of the upper waveguide wall with respect to the regular ionosphere level is taken into account. The field components on the boundary surfaces obey the Leontovich impedance conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr ≫1) integration along the direction perpendicular to the ray path, we transform this system to a system of one-dimensional integral equations. The system is solved numerically in the diagonal approximation, combining direct inversion of the Volterra integral operator and the subsequent iterations. The proposed method reduces the computer time required for solving the problem and is useful for the study of both small-scale and large-scale irregularities. We obtained estimates of the TE field components that are not excited by the source considered and originate entirely from field scattering by a three-dimensional irregularity disturbing the geometric regularity of the ionospheric waveguide wall. State University of St. Petersburg, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 617–629, July, 2000.     

Towards a field theory of the plateau transitions in the integer quantum Hall effect

We suggest a procedure for calculating correlation functions of the local densities of states (DOS) at the plateau transitions in the integer quantum Hall effect (IQHE). We argue that their correlation functions are appropriately described in terms of the SL( )/SU(2) WZNW model (at the usual Ka –Moody point and with the level 6≤k≤8 ). In this model we have identified the operators corresponding to the local DOS, and derived the partial differential equation determining their correlation functions. The OPEs for powers of the local DOS obtained from this equation are in agreement with available results.     

Elimination of Diurnal,Annual, and Solar Variations in the Matrix Observations of the URAGAN Muon Hodoscope

Physics of Atomic Nuclei - A method for elimination of periodical diurnal, annual, and 27-day and 11-year solar variations in the matrix observations of the URAGAN muon hodoscope was developed. The...     

Bi-SQUID arrays and parallel SQIF structures for active electrically small antennas

The basic physics of the development of broadband active electrically small superconductive antennas for the subgigahertz and gigahertz frequency ranges, based on series arrays with cells characterized by a highly linear voltage response to the magnetic component B of an electromagnetic signal, are under consideration. As such cells, bi-SQUIDs and cells based on two parallel SQIF structures that are differentially connected are proposed. Series arrays of cells with linear voltage response, including an antenna prototype, are fabricated using standard niobium technology with a critical current density of Josephson junctions of 4.5 kA/cm² and are studied experimentally. The data obtained allow estimation of the achievable dV/dB conversion factor and the sensitivity ??B for an antenna integrated with a magnetic flux converter, placed on an available area of 3.3 × 3.3 mm of a chip 5 × 5 mm in size. These values are found to be 10 ??V/nT and 20 fT/Hz^1/2, respectively. The conversion factor increases in proportion with the area a ² occupied by the antenna with a square flux converter, and the sensitivity is improved as a ^?3/2.     

Gamma deexcitation of the 180m Ta isomer

Vibrational states built on the K ^π = 9^? isomer and on the ground state (K ^π = 1⁺) in ¹⁸⁰Ta are calculated within the quasiparticle-phonon nuclear model using the ¹⁷⁸Hf nucleus as a core. A procedure for calculating the rates of K-allowed γ-ray transitions from vibrational states built on the isomer to those built on the ground state is presented. The probabilities of two-step processes consisting of a dipole excitation of the isomer and successive E1 and E2 transitions from them to vibrational states built on the ground state of the ¹⁸⁰Ta nucleus are calculated. Two-step transitions from the isomer to vibrational states below 2.7 MeV and to the vibrational states built on the ground state appear to be very weak. There are many E1 transitions from the vibrational states built on the isomer to the vibrational states built on the ground state. They are weak and cannot be responsible for the strong deexcitation of ^180m Ta in the relevant (γ, γ′) reaction. A decisive role is played by collective E2 transitions from dipole excitations in several excitation energy intervals ranging between 2.7 and 4.0 MeV. These highly intense K-allowed two-step γ-ray transitions can be responsible for the strong deexcitation of the ^180m Ta state in the (γ, γ′) reactions.     

Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals

We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and analytic functionals with a tempered growth. We prove that Lorentz-covariant functionals with essential singularities can be decomposed into polynomial covariants and establish the possibility of the invariant decomposition of their carrier cones. We describe the properties of odd highly singular generalized functions. These results are used to investigate the vacuum expectation values of nonlocal quantum fields with an arbitrary high-energy behavior and to extend the spin–statistics theorem to nonlocal field theory.