Bethe Subalgebras in Twisted Yangians

We study analogues of the Yangian of the Lie algebra $gl_N$ for the other classical Lie algebras $so_N$ and $sp_N$. We call them twisted Yangians. They are coideal subalgebras in the Yangian $Y(gl_N)$ of $gl_N$ and admit homomorphisms onto the universal enveloping algebras $U(so_N)$ and $U(sp_N)$ respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in $U(so_N)$ and $U(sp_N)$ of these subalgebras are also maximal commutative.Comment: 26 pages, amstex, misprints correcte

Hall Transport in Granular Metals and Effects of Coulomb Interactions

We present a theory of Hall effect in granular systems at large tunneling conductance $g_{T}\gg 1$. Hall transport is essentially determined by the intragrain electron dynamics, which, as we find using the Kubo formula and diagrammatic technique, can be described by nonzero diffusion modes inside the grains. We show that in the absence of Coulomb interaction the Hall resistivity $\rho_{xy}$ depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the grains and type of granular lattice. Further, we study the effects of Coulomb interactions by calculating first-order in $1/g_T$ corrections and find that (i) in a wide range of temperatures T \gtrsim \Ga exceeding the tunneling escape rate \Ga, the Hall resistivity $\rho_{xy}$ and conductivity \sig_{xy} acquire logarithmic in $T$ corrections, which are of local origin and absent in homogeneously disordered metals; (ii) large-scale ``Altshuler-Aronov'' correction to \sig_{xy}, relevant at T\ll\Ga, vanishes in agreement with the theory of homogeneously disordered metals.Comment: 29 pages, 16 figure

Investigation of glycation products by THz time-domain spectroscopy

Glycation is the non-enzymatic reaction betwee

Cherednik algebras and Zhelobenko operators

We study canonical intertwining operators between induced modules of the trigonometric Cherednik algebra. We demonstrate that these operators correspond to the Zhelobenko operators for the affine Lie algebra of type A. To establish the correspondence, we use the functor of Arakawa, Suzuki and Tsuchiya which maps certain modules of the affine Lie algebra to modules of the Cherednik algebra

A comprehensive study of albumin solutions in the extended terahertz frequency range

Sensitivity of the THz frequency range to the solutions of biomolecules originates from the decrease of absorption and dispersion of water in its bound state. Correct measurement and interpretation of the THz spectra of water-containing samples is still a challenging task because the reliable relaxation model for such spectra is not well established. The transmission and the attenuated total internal reflection geometries data were combined for precise analysis of the spectra of the aqueous solutions of bovine serum albumin within the range 0.05–3.2 THz. We compare the concentration dependencies of the dielectric function at “low,” “middle,” and “high” frequency and do not confirm an anomalous increase in absorption for concentrations below 17 mg/mL published by other teams

A comprehensive study of albumin solutions in the extended terahertz frequency range

Sensitivity of the THz frequency range to the solutions of biomolecules originates from the decrease of absorption and dispersion of water in its bound state. Correct measurement and interpretation of the THz spectra of water-containing samples is still a challenging task because the reliable relaxation model for such spectra is not well established. The transmission and the attenuated total internal reflection geometries data were combined for precise analysis of the spectra of the aqueous solutions of bovine serum albumin within the range 0.05–3.2 THz. We compare the concentration dependencies of the dielectric function at “low,” “middle,” and “high” frequency and do not confirm an anomalous increase in absorption for concentrations below 17 mg/mL published by other teams

Influence of split-ring resonators on the terahertz transmission of a planar waveguide

Terahertz transmission spectra of subwavelength split-ring resonator structures on ceramic substrates are investigated experimentally. For terahertz wave propagation along the ring resonators used as one of the faces of a planar dielectric waveguide, enhanced transmission is detected near the LC-resonance frequency. Dependences of the resonant absorption frequencies on the geometric structure characteristics are found for normal terahertz wave propagation through the structures