Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates

Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the literature, but here they are characterized in full generality together with their integrability properties. Some of these systems are defined only in a region of $\mathbb R^n$, and in general they do not include bounded solutions. The quantum symmetries and potentials are shown to reduce to their superintegrable classical analogs in the $\hbar \to0$ limit.Comment: 23 Pages, 3 figures, To appear in Nonlinearit

Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians

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Superintegrability of the Fock-Darwin system

The Fock-Darwin system is analysed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.Comment: 21 pages,16 figure

Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems

Producción CientíficaLadder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two ‘factor functions’. We apply this method to the curved Kepler–Coulomb and Rosen–Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the systems.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y León-FEDER (projects BU229P18 / VA057U16 / VA137G18)

The use of combination therapy in pulmonary arterial hypertension: new developments

There is a strong clinical rationale for combination therapy in pulmonary arterial hypertension (PAH), as several pathological pathways have been implicated in its pathogenesis and no single agent has yet been shown to deliver completely satisfactory results. Registry data indicate that use of combination therapy is in fact common in existing clinical practice, even though support has been largely empirical or derived from small-scale observational studies. Data from large, adequately powered, randomised controlled trials of combination therapy in PAH are now emerging and suggest that combination therapy may be clinically beneficial. Studies of bosentan in combination with prostanoids and phosphodiesterase (PDE)-5 inhibitors show consistent evidence of improvements in exercise capacity compared with placebo. Similar improvements have been observed with PDE-5 inhibitors in combination with prostanoids. The appropriate timing of combination therapy requires further evaluation but goal-oriented therapy using combinations of oral and inhaled drugs has been shown to provide acceptable long-term results in patients with advanced PAH. Monitoring should be performed regularly and be based on repeatable, noninvasive, measurable parameters that have prognostic value