New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

We propose new formulas for eigenvectors of the Gaudin model in the \sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula $| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>$, where $w_1$, $w_2$ fulfil the standard well-know Bethe Ansatz equations

Exchange couplings in the magnetic molecular cluster Mn12Ac

The magnetic properties of the molecular cluster Mn12Ac are due to the four Mn3+ ions which have spins S=3/2 and the eight Mn4+ ions with spins S=2. These spins are coupled by superexchange mechanism. We determine the four exchange couplings assuming a Heisenberg-type interaction between the ions. We use exact diagonalization of the spin Hamiltonian by a Lanczos algorithm and we adjust the couplings to reproduce the magnetization curve of Mn12Ac. We also impose the constraint of reproducing a gap of 35K between a S=10 ground state and a first excited state with S=9. We predict that there is an excited level with S=8 at 37K above the ground state, only slightly above the S=9 excited state which lies at 35K and the next excited state is a S=9 multiplet at 67K above the S=10 ground state.Comment: 15 pages, 6 figures, submitted to Phys Rev B, corrected a misTeX: values of J1, J2 have changed, refs update

On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation of these curves. They build up a system of cuts modeling the spectral curve as a two sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.Comment: 16 page

Pyrimido[1,2-a]benzimidazoles: synthesis and perspective of their pharmacological use

[Figure not available: see fulltext.] The review presents data on the synthesis as well as studies of biological activity of new derivatives of pyrimido[1,2-a]benzimidazoles published over the last decade. The bibliography of the review includes 136 sources. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.The reported study was funded the RFBR, project No. 19-33-90161

Spectral properties of the t-J model in the presence of hole-phonon interaction

We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The $t$-$J$ model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant $g$ is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasi-particle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multi-magnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron- phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small.Comment: REVTeX, 20 pages, 9 figures, to be published in Phys. Rev. B (Nov. 1, 1996

YARN begins

В статье представлен проект создания большого открытого тезауруса русского языка YARN (Yet Another RussNet). Основная особенность проекта — использование wiki-подхода к наполнению и редактированию ресурса. В статье описаны лингвистические принципы создания тезауруса YARN, формат данных, а также ближайшие практические шаги, которые планируется предпринять в рамках проекта.YARN (Yet Another RussNet) is a work-in-progress on development of a large and open WordNet-like thesaurus for Russian. The paper reports on linguistic design, development and organizational principles, and interchange format of YARN.Исследование осуществляется при финансовой поддержке РГНФ (проект № 13-04-12020 «Новый открытый электронный тезаурус русского языка»). Мы благодарим участников группы yarn_org за активность, замечания и предложения. Работа Андрея Крижановского выполнена при частичной финансовой поддержке РФФИ (проект № 11-01-00251, № 12-01-00481, № 12-07-00070) и РГНФ (проект № 12-04-12062). Работа Ольги Ляшевской и Анастасии Бонч-Осмоловской отражает результаты исследований, проведенных при поддержке Программы фундаментальных исследований НИУ Высшая школа экономики (2013), проект «Корпусные технологии в лингвистических и междисциплинарных исследованиях». Павел Браславский благодарит группу разработчиков GermaNet под руководством проф. Эрхарда Хинрихса из университета Тюбингена за гостеприимство, плодотворное обсуждение проекта и обмен опытом, а также MUMIA Network30 за финансовую поддержку визита в Тюбинген в рамках программы Short Term Scientific Missions (STSM)

Manin matrices and Talalaev's formula

We study special class of matrices with noncommutative entries and demonstrate their various applications in integrable systems theory. They appeared in Yu. Manin's works in 87-92 as linear homomorphisms between polynomial rings; more explicitly they read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}]=[M_{kj}, M_{il}]$ (e.g. $[M_{11}, M_{22}]=[M_{21}, M_{12}]$). We claim that such matrices behave almost as well as matrices with commutative elements. Namely theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) holds true for them. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and the so--called Cartier-Foata matrices. Also, they enter Talalaev's hep-th/0404153 remarkable formulas: $det(\partial_z-L_{Gaudin}(z))$, det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g in the construction of new generators in $Z(U(\hat{gl_n}))$ (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also discuss applications to the separation of variables problem, new Capelli identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints e.g. in Newton id-s fixed, normal ordering convention turned to standard one, refs. adde