Slavnov and Gaudin-Korepin Formulas for Models without U(1){\rm U}(1) Symmetry: the Twisted XXX Chain

We consider the XXX spin-$\frac{1}{2}$ Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without ${\rm U}(1)$ symmetry characterized by an inhomogenous Baxter T-Q equation

The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains

A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider D_{n+1}^(2) chains with other integrable boundary conditions, which do not have quantum group symmetry.Comment: 47 pages; v2: two references added and minor change

A tale of two Bethe ans\"atze

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov's construction. A simple explicit relation between the eigenvectors from the two Bethe ans\"atze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.Comment: 28 pages; v2: 30 pages, added proof of (4.40) and (5.39), minor changes to match the published versio

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators

Direct Experimental Evidence of Exciton-Phonon Bound States in Carbon Nanotubes

We present direct experimental observation of exciton-phonon bound states in the photoluminescence excitation spectra of isolated single walled carbon nanotubes in aqueous suspension. The photoluminescence excitation spectra from several distinct single-walled carbon nanotubes show the presence of at least one sideband related to the tangential modes, lying {200 meV} above the main absorption/emission peak. Both the energy position and line shapes of the sidebands are in excellent agreement with recent calculations [PRL {\bf 94},027402 (2005)] that predict the existence of exciton-phonon bound states, a sizable spectral weight transfer to these exciton-phonon complexes and that the amount of this transfer depends on the specific nanotube structure and diameter. The observation of these novel exciton-phonon complexes is a strong indication that the optical properties of carbon nanotubes have an excitonic nature and also of the central role played by phonons in describing the excitation and recombination mechanisms in carbon nanotubes