Highest coefficient of scalar products in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.Comment: 17 page

On factorizing FF-matrices in Y(sln)Y(sl_n) and Uq(sln^)U_q(\hat{sl_n}) spin chains

We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de Santos, we derive a completely factorized expression for the $F$-matrix of such models and prove its equivalence to the expression obtained by Albert, Boos, Flume and Ruhlig. A new relation between the $F$-matrices and the Bethe eigenvectors of these spin chains is given.Comment: 30 page

Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in diamond anvil cell. Application to the stability study of AlPdMn

We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows to accurately measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this new experimental technique is demonstrated in studies of lattice dynamics, stability domain and relaxation process in a metallic sample, a perfect single-grain AlPdMn quasicrystal, and rare gas, neon and argon. Application to the study of defect-induced lattice stability in AlPdMn up to 30 GPa is proposed. The present work has potential for application in areas ranging from fundamental problems in physics of solid and liquid state, which in turn could be beneficial for various other scientific fields as Earth and planetary science or material research

Generalized q-Onsager Algebras and Dynamical K-matrices

A procedure to construct $K$-matrices from the generalized $q$-Onsager algebra \cO_{q}(\hat{g}) is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to dynamical (non-c-number) solutions. It shows the relation between soliton non-preserving reflection equations or twisted reflection equations and the generalized $q$-Onsager algebras. These dynamical $K$-matrices are important to quantum integrable models with extra degrees of freedom located at the boundaries: for instance, in the quantum affine Toda field theories on the half-line they yield the boundary amplitudes. As examples, the cases of \cO_{q}(a^{(2)}_{2}) and \cO_{q}(a^{(1)}_{2}) are treated in details

Central extension of the reflection equations and an analog of Miki's formula

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.

Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.Comment: 15 pages, proceeding for Dubna International SQS 09 Worksho

On Form Factors in nested Bethe Ansatz systems

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.Comment: 34 pages, v2 (minor modifications

Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices (K^+(u),K^-(u)). The nested Bethe anstaz applies for a general K^-(u), but a particular form of the K^+(u) matrix. The construction extends and unifies the results already obtained for open spin chains based on fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.Comment: 40 pages; examples of Bethe vectors added; Bethe equations for U_q(gl(2/2)) added; misprints correcte

Absence of a Fermi surface in classical minimal four-dimensional gauged supergravity

We demonstrate that the two point function of the supercurrent dual to the gravitino in the four-dimensional extremal anti-de Sitter Reissner-Nordstrom black hole does not exhibit a Fermi surface singularity. In our analysis, we utilize the ingoing Eddington-Finkelstein coordinate system, which enables us to bypass certain complications in the determination of the allowed near horizon behavior of the gravitino field at zero frequency. We check that our method agrees with previous results for the massless charged Dirac field.Comment: 12 pages, 1 figur

Stratégies démographiques des poissons des rivières françaises : premiers résultats

International audienceThe analysis of the biological, morphological and food characteristics of 35 French species leads to distinguish two main strategies. The first one gathers 11 species with a short life span and which maximize the survival of juveniles. Within it, cold water species with a long reproduction lifetime and thermophilous species with a relatively stronger fertility can be distinguished. Their diets are essentially made of insects- plankton and insects-fishes. In the second group, no care is given to juveniles; relative fertilities are higher and inversely correlated to the number of reproduction cycles. 10 species are omnivorous with a grass-wastes tendancy, and 4 species eat strictly fishes. The canonical analysis of correspondances shows that these biological characteristics are sufficuent to understand most of the longitudinal zonation.L'analyse des caractéristiques biologiques et morpho-alimentaires de 35 espèces françaises permet de distinguer 2 stratégies principales. La première rassemble 11 espèces à faible longévité et maximisant la survie des jeunes. En son sein, on distingue des espèces d'eau froide à longue durée de vie pré-reproductrice et des espèces thermophiles à fécondité relativement plus forte. Leurs régimes alimentaires sont essentiellement du type insectivore-planctonophage et insectivore-ichtyophage. Dans le second groupe, aucun soin n'est apporté aux jeunes ; les fécondités relatives sont plus fortes et inversement corrélées avec le nombre de cycles de reproduction. 10 espèces sont des omnivores à tendance herbivore-détritivore et 4 des ichtyophages stricts. L'analyse canonique des correspondances démontre que ces caractéristiques biologiques rendent compte de l'essentiel de la zonation longitudinale