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

Что и как спрашивают в социальных вопросно-ответных сервисах по-русски?

In our study we surveyed different approaches to the study of questions in traditional linguistics, question answering (QA), and, recently, in community question answering (CQA). We adapted a functional-semantic classification scheme for CQA data and manually labeled 2,000 questions in Russian originating from [email protected] CQA service. About half of them are purely conversational and do not aim at obtaining actual information. In the subset of meaningful questions the major classes are requests for recommendations, or how-questions, and fact-seeking questions. The data demonstrate a variety of interrogative sentences as well as a host of formally non-interrogative expressions with the meaning of questions and requests. The observations can be of interest both for linguistics and for practical applications

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

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

A Spinning Wheel for YARN: User Interface for a Crowdsourced Thesaurus

YARN (Yet Another RussNet) project started in 2013 aims at creating a large open thesaurus for Russian using crowdsourcing. This paper describes synset assembly interface developed within the project — motivation behind it, design, usage scenarios, implementation details, and first experimental results

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.

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