Using Sklyanin's classical theory of integrable boundary conditions, we use the Hamiltonian approach to derive new integrable boundary conditions for the Ablowitz-Ladik model on the finite and half infinite lattice. In the case of half infinite lattice, the special and new emphasis of this paper is to connect directly the Hamiltonian approach, based on the classical $r$-matrix, with the zero curvature representation and B\"acklund transformation approach that allows one to implement a nonlinear mirror image method and construct explicit solutions. It is shown that for our boundary conditions, which generalise (discrete) Robin boundary conditions, a nontrivial extension of the known mirror image method to what we call {\it time-dependent boundary conditions} is needed. A careful discussion of this extension is given and is facilitated by introducing the notion of intrinsic and extrinsic picture for describing boundary conditions. This gives the specific link between Sklyanin's reflection matrices and B\"acklund transformations combined with folding, {\it in the case of non-diagonal reflection matrices}. All our results reproduce the known Robin boundary conditions setup as a special case: the diagonal case. Explicit formulas for constructing multisoliton solutions on the half-lattice with our time-dependent boundary conditions are given and some examples are plotted.

Première femme à avoir accédé au rang de professeur titulaire au Massachussetts Institute of Technology (MIT),Mildred Spiewak Dresselhaus, ou simplement Millie pourla plupart de ses collègues, est l’exemple d’un engagement passionnel et infatigable pour la science en général, la physique en particulier, et pour la reconnaissancede la place des femmes en science.Sa disparition le 20 février 2017 à l’âge de 86 ans, en pleine activité scientifique, a très profondément marqué les communautés de chercheurs engagés dansles nanosciences. Ses contributions à la compréhension du couplage entre propriétés électroniques,vibrationnelles et structurales, dans les différentes formesde carbone sont au centre du développement des nanomatériaux carbonés et de leurs applications.

The goal of this chapter is to review the main information derived from Raman spectroscopy on individual suspended (free-standing) chiralityidentified single-wall carbon nanotubes (SWCNTs) and double-wall carbonnanotubes (DWCNTs) with a special focus on the characteristics of their radial breathing modes and G modes, including their resonance conditions. ForSWCNTs, the different relationships between the radial breathing mode frequency and the inverse of the diameter illustrate the high sensitivity of individual suspended SWCNTs to their environmental conditions. The intrinsicprofiles of the optical longitudinal (LO) and transverse (TO) G modes are unambiguously identified both for metallic and semiconducting chiral and achiral SWCNTs, and the diameter dependence of the LO and TO frequencies are established. In DWCNTs, the intertube coupling, originating from the van der Waals interaction between the inner and outer tubes, plays an important role in determining the features/characteristics of the collectiveradial breathing-like modes and G modes.

In the absence of direct evidence of new physics, any ultraviolet theory can be reduced to its specific set of low-energy effective operators. As a case study, we derive the effective field theory for the seesaw extension of the Standard Model, with sterile neutrinos of mass $M>m_W$. We systematically compute all Wilson coefficients generated at one loop. Hence, it becomes straightforward to (i) identify the seesaw parameters compatible with the smallness of neutrino masses; (ii) compute precision lepton observables, which may be sensitive to scales as large as $M\sim 10^3$ TeV; and (iii) establish sharp correlations among those observables. We find that the flavour-conserving Wilson coefficients set an upper bound on the flavour-violating ones. The low-energy limits on $\mu\to e$ and $\tau\to e,\mu$ transitions suppress flavour violation in $Z$ and Higgs decays, as well as electric dipole moments, far beyond the experimental reach. The bounds from the universality of $G_F$ and the invisible $Z$ width are more stringent than present and future limits on $\tau\to e,\mu$ transitions. We also present a general spurion analysis, to compare the seesaw with different models, thus assessing the discriminating potential of the effective approach.

We propose simple freeze-in models where the observed dark matter abundance is explained via the decay of an electrically charged and/or coloured parent particle into Feebly Interacting Massive Particles (FIMP). The parent particle is long-lived and yields a wide variety of LHC signatures depending on its lifetime and quantum numbers. We assess the current constraints and future high luminosity reach of these scenarios at the LHC from searches for heavy stable charged particles, disappearing tracks, displaced vertices and displaced leptons. We show that the LHC constitutes a powerful probe of freeze-in dark matter and can further provide interesting insights on the validity of vanilla baryogenesis and leptogenesis scenarios.

We reconsider a one-parameter class of known solutions of the circle compactification of Romans six-dimensional half-maximal supergravity. The gauge-theory duals of these solutions are confining four-dimensional field theories. Their UV completions consist of the compactification on a circle of a higher-dimensional field theory that is flowing between two fixed points in five dimensions. We systematically study the bosonic fluctuations of the supergravity theory, corresponding to the bosonic glueballs of the dual field theory.We perform numerically the calculation of the spectrum of excitations of all the bosonic fields, several of which had been disregarded in earlier work on the subject. We discuss the results as a function of the one parameter characterising the class of background solutions, hence further extending known results. We show how certain towers of states are independent of the background, and compare these states to existing lattice literatureon four-dimensional Yang-Mills (pure) gauge theories, confirming the existence of close similarities.For the afore mentioned analysis, we construct gauge-invariant combinations of the fields appearing in the reduction to five dimensions of the supergravity theory, and hence focus on the 32 physical bosonic degrees of freedom. We show explicitly how to implement gauge-fixing of the supergravity theory. The results of such technical work could be used to analyse the spectra of other theories proposed in the context of top-down holography. For example, it could be applied to holographic realisations of composite-Higgs and lightdilaton scenarios.

The $sl_N$-Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the $sl_N$-Onsager algebra is given, its current algebra and commutative subalgebra are constructed. Certain quotients of the $sl_N$-Onsager algebra are then considered, which produce `classical' analogs of higher rank extensions of the Askey-Wilson algebra. As examples, the cases $N=3$ and $N=4$ are described in details.