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

Ion backflow studies with a triple-GEM stack with increasing hole pitch

Gas Electron Multipliers have undergone a very consistent development since their invention in 1997. Their production procedures have been tuned in such a way that nowadays it is possible to produce foils with areas of the order of the square meter that can operate at a reasonable gain, uniform over large areas and with a good stability in what concerns electrical discharges. For the third run of LHC, they will be included in the CMS and ALICE experiments after significant upgrades of the detectors, confirming that these structures are suitable for very large experiments. In the special case of Time Projection Chambers, the ion backflow and the energy resolution are sensitive issues that must be addressed and the GEM has shown to be able to deal with both of them. In this work, a stack of three GEMs with different pitches has been studied as a possible future approach for ion-backflow suppression to be used in TPCs and other detection concepts. With this approach, an ion backflow of 1 % with an energy resolution of 12 % at 5.9 keV has been achieved with the detector operating in an Ar/CO2 (90/10) mixture at a gain of ~ 2000.Comment: 15 pages, 11 figure

Topological mass generation to antisymmetric tensor matter field

We propose a mechanism to give mass to tensor matter field which preserve the U(1) symmetry. We introduce a complex vector field that couples with the tensor in a topological term. We also analyze the influence of the kinetic terms of the complex vector in our mechanism.Comment: 5 pages, to appear in Europhysics Letter