Bethe eigenvectors of higher transfer matrices

We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting operators on the tensor product, called the transfer matrices. We show that the Bethe vectors for these models, given by the algebraic nested Bethe ansatz are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.Comment: 48 pages, amstex.tex (ver 2.2), misprints correcte

On the low-temperature anomalies in the thermal conductivity of plastically deformed crystals due to phonon-kink scattering

Previous experimental studies of the thermal conductivity of plastically deformed lead crystals in the superconducting state have shown strong anomalies in the thermal conductivity. Similar effects were also found for the thermal conductivity of bent ${}^4\text{He}$ samples. Until now, a theoretical explanation for these results was missing. In this paper we will introduce the process of phonon-kink scattering and show that it qualitatively explains the anomalies that experiments had found.Comment: 3 pages, follow-up paper to appear soo

Gaudin models for gl(m|n)

Date of Acceptance: 16/04/2015We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra gl(m|n). In particular, we prove the completeness of the Bethe ansatz in the case of tensor products of fundamental representations.Peer reviewedFinal Accepted Versio

Quantum spin chains and integrable many-body systems of classical mechanics

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem for quantum Hamiltonians of the former models is closely related to a sort of inverse spectral problem for Lax matrices of the latter ones. For simplicity, we focus on the most transparent and familiar case of spin chains on N sites constructed by means of the GL(2)-invariant R-matrix. They are related to the classical Ruijsenaars-Schneider system of N particles, which is known to be an integrable deformation of the Calogero-Moser system. As an explicit example the case N=2 is considered in detail.Comment: 17 pages, misprints corrected, written for Proceedings of the International School and Workshop "Nonlinear Mathematical Physics and Natural Hazards", Sofia, Bulgaria, November 28 - December 2, 2013, to be published in Lecture Notes in Physic

High-field AFMR in single-crystalline La_{0.95}Sr_{0.05}MnO_3: Experimental evidence for the existence of a canted magnetic structure

High-field antiferromagnetic-resonance (AFMR) spectra were obtained in the frequency range 60 GHz < \nu < 700 GHz and for magnetic fields up to 8 T in twin-free single crystals of La_{0.95}Sr_{0.05}MnO_3. At low temperatures two antiferromagnetic modes were detected, which reveal different excitation conditions and magnetic field dependencies. No splitting of these modes was observed for any orientation of the static magnetic field excluding the phase-separation scenario for this composition. Instead, the full data set including the anisotropic magnetization can be well described using a two-sublattice model of a canted antiferromagnetic structure.Comment: 4 pages, 3 figure

Some recursive formulas for Selberg-type integrals

A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur integrals whenever the Kostka numbers relating Schur functions and the corresponding monomial polynomials are explicitly known. We illustrate the usefulness of our results discussing some interesting examples.Comment: 11 pages. To appear in Jour. Phys.

Determination of Ethanol Content in Fuels with Phononic Crystal Sensor

Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons.Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons

Wood-decaying Basidiomycetes Associated with Dwarf Siberian Pine in Northeast Siberia and the Kamchatka Peninsula

A survey of the biodiversity of wood-decaying Basidiomycetes associated with Pinus pumila (the dwarf Siberian pine), a highly characteristic woody plant of Northeast Siberia and the Kamchatka Peninsula, is presented for the first time. Thirty-two species of wood-decaying Basidiomycetes were recorded in the area for this tree, ofwhich twenty-seven were described the first time: 19 species in the Magadan region and 9 in the Kamchatka Peninsula. Communities of wood-decaying fungi associated with P. pumila have low biodiversity and consist of 16 species in the Kamchatka Peninsula and 21 species in the Magadan region, with only 5 of them being common to both areas. All fungi associated with dwarf Siberian pine belong to widespread species and are not specialized to this tree: they are extremely low in numbers and their composition strongly varies in different habitats. This shows that this tree does not have its own specialized and stable complex of wood-decaying Basidiomycetes. Keywords: biodiversity, Czekanowski-Sørensen index, host-specializatio