Transition Radiation of Moving Abrikosov Vortices

We show that Abrikosov vortices moving towards the surface of a superconductor emit electromagnetic radiation into free space. The frequency distribution of the radiated intensity displays a pronounced maximum at microwave frequencies around v_x/lambda, where lambda is the magnetic penetration length. Coherent motion of a lattice of flux lines leads to constructive interference and increases the strength of the radiated power by a large factor.Comment: 4 pages, 1 figure The new version includes a derivation of novel dynamical London equations for a moving Abrikosov vortex, as well as a detailed discussion of boundary condition

In-Plane Spectral Weight Shift of Charge Carriers in YBa2Cu3O6.9YBa_2Cu_3O_{6.9}

The temperature dependent redistribution of the spectral weight of the $CuO_2$ plane derived conduction band of the $YBa_2Cu_3O_{6.9}$ high temperature superconductor (T_c = 92.7 K) was studied with wide-band (from 0.01 to 5.6 eV) spectroscopic ellipsometry. A superconductivity - induced transfer of the spectral weight involving a high energy scale in excess of 1 eV was observed. Correspondingly, the charge carrier spectral weight was shown to decrease in the superconducting state. The ellipsometric data also provide detailed information about the evolution of the optical self-energy in the normal and superconducting states

Cosmology and New Physics

A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the main cosmological parameters are achieved through many independent physical phenomena and this minimizes possible interpretation errors. It is shown that astronomy demands new physics beyond the frameworks of the (minimal) standard model in particle physics. More revolutionary modifications of the basic principles of the theory are also discussed.Comment: 37 pages, 5 figures; lectures presented at 9th International Moscow School of Physics (34th ITEP Winter School

Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients

We consider a one-dimensional second-order elliptic equation with a high-dimensional parameter in a hypercube as a parametric domain. Such a problem arises, for example, from the Karhunen–Loève expansion of a stochastic PDE posed in a one-dimensional physical domain. For the discretization in the parametric domain we use the collocation on a tensor-product grid. The paper is focused on the tensor-structured solution of the resulting multiparametric problem, which allows to avoid the curse of dimensionality owing to the use of the separation of parametric variables in the tensor train and quantized tensor train formats. We suggest an efficient tensor-structured preconditioning of the entire multiparametric family of one-dimensional elliptic problems and arrive at a direct solution formula. We compare this method to a tensor-structured preconditioned GMRES solver in a series of numerical experiments.</p

Problems with Jumping Coefficients

We study separability properties of solutions of elliptic equations with piecewise constant coefficients in R d, d ≥ 2. Besides that, we develop efficient tensor-structured preconditioner for the diffusion equation with variable coefficients. It is based only on rank structured decomposition of the tensor of reciprocal coefficient and on the decomposition of the inverse of the Laplacian operator. It can be applied to full vector with linear-logarithmic complexity in the number of unknowns N. It also allows lowrank tensor representation, which has linear complexity in dimension d, hence, it gets rid of the “curse of dimensionality ” and can be used for large values of d. Extensive numerical tests are presented. AMS Subject Classification: 65F30, 65F50, 65N35, 65F10 Key words: structured matrices, elliptic operators, Poisson equation, matrix approximations

On the T-dependence of the magnetic penetration depth in unconventional superconductors at low temperatures: can it be linear?

We present a thermodynamics argument against a strictly linear temperature dependence of the magnetic penetration depth, which applies to superconductors with arbitrary pairing symmetry at low temperatures.Comment: 5 pages, expanded version of cond-mat/971102

Normal state resistivity of Ba1−x_{1-x}Kx_xFe2_2As2_2: evidence for multiband strong-coupling behavior

We present theoretical analysis of the normal state resistivity in multiband superconductors in the framework of Eliashberg theory. The results are compared with measurements of the temperature dependence of normal state resistivity of high-purity Ba$_{0.68}$K$_{0.32}$Fe$_{2}$As$_{2}$ single crystals with the highest reported transition temperature $T_c$ = 38.5 K. The experimental data demonstrate strong deviations from the Bloch-Gr\"{u}neisen behavior, namely the tendency to saturation of the resistivity at high temperatures. The observed behavior of the resistivity is explained within the two band scenario when the first band is strongly coupled and relatively clean, while the second band is weakly coupled and is characterized by much stronger impurity scattering.Comment: 4 pages, 3 figures, to be published in JETP Letters Vol.94, N