Integrable mixing of A_{n-1} type vertex models

Given a family of monodromy matrices {T_u; u=0,1,...,K-1} corresponding to integrable anisotropic vertex models of A_{(n_u)-1}-type, we build up a related mixed vertex model by means of glueing the lattices on which they are defined, in such a way that integrability property is preserved. Algebraically, the glueing process is implemented through one dimensional representations of rectangular matrix algebras A(R_p,R_q), namely, the `glueing matrices' zeta_u. Here R_n indicates the Yang-Baxter operator associated to the standard Hopf algebra deformation of the simple Lie algebra A_{n-1}. We show there exists a pseudovacuum subspace with respect to which algebraic Bethe ansatz can be applied. For each pseudovacuum vector we have a set of nested Bethe ansatz equations identical to the ones corresponding to an A_{m-1} quasi-periodic model, with m equal to the minimal range of involved glueing matrices.Comment: REVTeX 28 pages. Here we complete the proof of integrability for mixed vertex models as defined in the first versio

Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is $\frak{so}(3,1)$ and the SGA is $\frak{so}(4,2)$. We start with a representation of $\frak{so}(4,2)$ by functions on a realization of the Lobachevski space given by a two sheeted hyperboloid, where the Lie algebra commutators are the usual Poisson-Dirac brackets. Then, introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and "naive" ladder operators are identified. The previously defined "naive" ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non self-adjoint function of a linear combination of the ladder operators which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of two sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.Comment: 23 page

R-matrix presentation for (super)-Yangians Y(g)

We give a unified RTT presentation of (super)-Yangians Y(g) for so(n), sp(2n) and osp(m|2n).Comment: 9 page

Shot-noise-limited spin measurements in a pulsed molecular beam

Heavy diatomic molecules have been identified as good candidates for use in electron electric dipole moment (eEDM) searches. Suitable molecular species can be produced in pulsed beams, but with a total flux and/or temporal evolution that varies significantly from pulse to pulse. These variations can degrade the experimental sensitivity to changes in spin precession phase of an electri- cally polarized state, which is the observable of interest for an eEDM measurement. We present two methods for measurement of the phase that provide immunity to beam temporal variations, and make it possible to reach shot-noise-limited sensitivity. Each method employs rapid projection of the spin state onto both components of an orthonormal basis. We demonstrate both methods using the eEDM-sensitive H state of thorium monoxide (ThO), and use one of them to measure the magnetic moment of this state with increased accuracy relative to previous determinations.Comment: 12 pages, 6 figure

Favipiravir vs. Deferiprone: Tautomeric, photophysical, in vitro biological studies, and binding interactions with SARS-Cov-2-MPro/ACE2

Coronavirus disease 2019 (COVID-19) still remains the most disastrous infection continuously affecting millions of people worldwide. Herein, we performed a comparative study between the anti-influenza drug favipiravir (FAV) and the anti-thalassemia drug deferiprone (DFP) in order to examine their potential as basic scaffolds for the generation of most effective and structurally novel antivirals. To conduct the initial molecular modelling and virtual screening steps, our recently proposed single crystal X-ray diffraction (SCXRD)/HYdrogen DEssolvation (HYDE) technology platform has been used. This platform allows molecular design, interactive prioritization and virtual evaluation of newly designed molecules, simultaneously affecting two COVID-related targets, including angiotensin-converting enzyme 2 (ACE2) as a host-cellular receptor (host-based approach) and the main protease (Mpro) enzyme of the spike glycoprotein of SARS-Cov-2 (virus-based approach). Based on the molecular docking results, DFP has shown higher binding affinity (Ki HYDE values) over FAV towards both biological targets. The tautomeric, physicochemical, and biological properties of FAV and DFP have been studied both experimentally and theoretically using molecular spectroscopy (UV–VIS absorption), parallel artificial membrane permeability assay, and cell biology (PAMPA and MTT assay), as well as DFT quantum chemical calculations. According to the obtained results, the enol tautomers of both compounds are considerably more stable in different organic solvents. However, the keto tautomer of FAV was estimated to be most preferable under physiological conditions, which is in good agreement with the molecular docking studies. The isolated crystal structure of DFP is in an excellent agreement with the computation in respect of the most stable tautomer. Combined single X-ray/molecular modeling studies including HYDE analyses provided not only insights into the protein–ligand interactions within the binding site of SARS-Cov-2-ACE2 and SARS-Cov-2-Mpro, but also a valuable information regarding the most stable enol tautomeric form of DFP that contributes to its estimated higher potency against these targets

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.Comment: 24 page

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We have promoted a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw's particles with the same chirality which spectrum is a vacuum-like one. As another conflictive result we have proved that a Wess-Zumino term used in the literature consists of the scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system.Comment: 6 pages, Revtex. Final version to appear in Physical Review

Spin physics with antiprotons

New possibilities arising from the availability at GSI of antiproton beams, possibly polarised, are discussed. The investigation of the nucleon structure can be boosted by accessing in Drell-Yan processes experimental asymmetries related to cross-sections in which the parton distribution functions (PDF) only appear, without any contribution from fragmentation functions; such processes are not affected by the chiral suppression of the transversity function $h_1(x)$. Spin asymmetries in hyperon production and Single Spin Asymmetries are discussed as well, together with further items like electric and magnetic nucleonic form factors and open charm production. Counting rates estimations are provided for each physical case. The sketch of a possible experimental apparatus is proposed.Comment: Presented for the proceedings of ASI "Spin and Symmetry", Prague, July 5-10, 2004, to be published in Czech. J. Phys. 55 (2005