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

An eco-geomorphic model of tidal channel initiation and elaboration in progressive marsh accretional contexts

The formation and evolution of tidal networks have been described through various theories which mostly assume that tidal network development results from erosional processes, therefore emphasizing the chief role of external forcing triggering channel net erosion such as tidal currents. In contrast, in the present contribution we explore the influence of sediment supply in governing tidal channel initiation and further elaboration using an ecogeomorphic modeling framework. This deliberate choice of environmental conditions allows for the investigation of tidal network growth and development in different sedimentary contexts and provides evidences for the occurrence of both erosional and depositional channel-forming processes. Results show that these two mechanisms in reality coexist but act at different time scales: channel initiation stems from erosional processes, while channel elaboration mostly results from depositional processes. Furthermore, analyses suggest that tidal network ontogeny is accelerated as the marsh accretional activity increases, revealing the high magnitude and prevalence of the depositional processes in governing the morphodynamic evolution of the tidal network. On a second stage, we analyze the role of different initial topographic configurations in driving the development of tidal networks. Results point out an increase in network complexity over highly perturbed initial topographic surfaces, highlighting the legacy of initial conditions on channel morphological properties. Lastly, the consideration that landscape evolution depends significantly on the parameterization of the vegetation biomass distribution suggests that the claim to use uncalibrated models for vegetation dynamics is still questionable when studying real cases

Évolution à long terme du peuplement piscicole du bassin de la Seine

Des données anciennes issues de la littérature sont utilisées pour apprécier les conséquences des activités humaines sur l'évolution de la structure des communautés piscicoles du bassin de la Seine

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

Quantifying the physical alterations of river reaches using a regional river morphology reference model. A step towards river restoration.

River engineeringRiver habitat management and restoratio

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

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.

Direct Observation of Propagating Gigahertz Coherent Guided Acoustic Phonons in Free Standing Single Copper Nanowires

We report on gigahertz acoustic phonon waveguiding in free-standing single copper nanowires studied by femtosecond transient reflectivity measurements. The results are discussed on the basis of the semianalytical resolution of the Pochhammer and Chree equation. The spreading of the generated Gaussian wave packet of two different modes is derived analytically and compared with the observed oscillations of the sample reflectivity. These experiments provide a unique way to independently obtain geometrical and material characterization. This direct observation of coherent guided acoustic phonons in a single nano-object is also the first step toward nanolateral size acoustic transducer and comprehensive studies of the thermal properties of nanowires

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