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

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

Integrable Models From Twisted Half Loop Algebras

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaudin magnets, and Calogero-type models of particles on several half-lines meeting at a point.Comment: 22 pages, 1 figure, Introduction improved, References adde

Morphological characteristic during third week experimental nephrolithiasis model

The results of kidney medulla morphological study from Wistar rats with ethylenglycol oxalate nephrolithiasis model are analyzed. Alteration of internal and external medulla, microliths allocation characteristics are evaluated

Black Silicon with high density and high aspect ratio nanowhiskers

Physical properties of black Silicon (b-Si) formed on Si wafers by reactive ion etching in chlorine plasma are reported in an attempt to clarify the formation mechanism and the origin of the observed optical and electrical phenomena which are promising for a variety of applications. The b-Si consisting of high density and high aspect ratio sub-micron length whiskers or pillars with tip diameters of well under 3 nm exhibits strong photoluminescence (PL) both in visible and infrared, which are interpreted in conjunction with defects, confinement effects and near band-edge emission. Structural analysis indicate that the whiskers are all crystalline and encapsulated by a thin Si oxide layer. Infrared vibrational spectrum of Si-O-Si bondings in terms of transverse-optic (TO) and longitudinal-optic (LO) phonons indicates that disorder induced LO-TO optical mode coupling can be an effective tool in assessing structural quality of the b-Si. The same phonons are likely coupled to electrons in visible region PL transitions. Field emission properties of these nanoscopic features are demonstrated indicating the influence of the tip shape on the emission. Overall properties are discussed in terms of surface morphology of the nano whiskers

Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra U(\g) of a semisimple Lie algebra \g. This family is parameterized by collections of pairwise distinct complex numbers $z_1,...,z_n$. We obtain some new commutative subalgebras in U(\g)^{\otimes n} as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the hamiltonians of bending flows and to the Gelfand--Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.Comment: 11 pages, references adde

Benchmarking of Uranium-238 Evaluations against Spherical Transmission and (n,xn)-Reaction Experimental Data

Abstract. The double differential cross sections for the U(n,xn) reaction at 14 MeV and neutron leakage spectra from the uranium sphere of 24 cm outer and 8 cm inner diameters with the central T-D and 252 Cf neutron sources measured at the Institute of Physics and Power Engineering were used for benchmarking the evaluated cross sections from ENDF-B6, JEFF-3.0, and "Maslov" libraries and preliminary versions of JEFF-3.1 and ENDF-B7 evaluations for 238 U