Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

Se and I status in pregnant ewes from a pastoral system and the effect of supplementation with Se and I or only Se on wool quality of lambs

Australian Merino ewes and lambs producing fine fibre wool for export are raised in the north-west of Uruguay in pasture-based systems. We studied the status of selenium and iodine in pregnant Merino ewes (10 per treatment) grazing in natural pasture, in natural pasture and supplemented with Se (0.1 mg Se/kg dry matter intake) and I (1 mg I/kg dry matter intake), or in natural pasture and supplemented with Se alone (0.1 mg Se/kg dry matter intake), during the last 30 days of gestation. Further, we evaluated the performance and wool quality of their offspring. Content of Se and I in natural pasture, in the sera of pregnant ewes, and in the wool of their offspring and levels of thyroidal hormones—TSH, T4, and free T3 (FT3)—in the sera of pregnant ewes were determined. The performance of lambs and the commercial parameters of fine fibre wool produced were measured. Results showed normal Se levels in serum (0.12–0.15 mg/l) in the ewes grazing in natural pasture (0.07–0.09 mg/kg DM) during late pregnancy. The observed increase in Se content in the pasture at lambing (0.11–0.16 mg/kg DM) improved serum Se levels (0.216 mg/l); however, the serum levels were not affected by the supplementation. I content in pasture showed adequate levels (0.50–0.60 mg/kg DM), which were reflected in the blood serum values 30 days prior to lambing (0.197–0.208 mg/l). However, at lambing, the I content in blood serum decreased (0.150 mg/l). Further, the supplementation did not modify the serum I levels (0.163–0.175 mg/l). An increase in FT3 levels in ewes at lambing could be associated with the increase in Se content in pasture and/or the adequate I content in pasture. No effect of supplementation was observed. Lambs showed good results regarding the quality of fine fibre wool and performance after supplementation with Se and I or Se alone and exhibited slightly improved Se and I content in wool. In conclusion, natural pasture provides adequate status in Se and I for the Merino ewes and their offspring without any additional beneficial effects of supplementation with Se and I or only Se

On the geometry of closed G2-structure

We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kahler geometry. The result was generalized by R.L.Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main theorem is generalized to the assumption that the Weyl tensor is divergence-free, clarity improved, typos correcte

Entropy, Topological Theories and Emergent Quantum Mechanics

[EN] The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.Research supported by grant No. ENE2015-71333-R (Spain).Cabrera, D.; Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Vazquez Molina, J. (2017). Entropy, Topological Theories and Emergent Quantum Mechanics. Entropy. 19(3). https://doi.org/10.3390/e19030087S19

Extended WKB method, resonances and supersymmetric radial barriers

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.Comment: 12 pages, 4 figures, 3 table

The G_2 sphere over a 4-manifold

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-calibrated if, and only if, M is an Einstein manifold. The fibres are always associative. In fact, the associated 3-form results from a linear combination of three other volume 3-forms, one of which is the volume of the fibres. We also give new examples of co-calibrated structures on well known spaces. We hope this contributes both to the knowledge of special geometries and to the study of 4-manifolds.Comment: 13 page

Morteros de albañilería con escombros de demolición

The possibility of recycling construction rubble, its technical and economic effectiveness, and the social and ecological impact they provide for our society is the reason and the starting point for an optimal exploitation of this aggregate in the manufacture of masonry mortar, since it has the same inherent properties as those obtained from the quarry aggregates, described in the Cuban standard NC52-79:93. The work consists in the preparation and study of masonry mortars using recycled aggregates -demolition product-. Four volumetric dosages were prepared (1:4; 1:5; 1:6 y 1:8), which were submitted to physical and mechanical tests at 7, 28 and 60 days, adherence resistance at 28 days, and capillary absorption, obtaining similar results to those.La posibilidad real del reciclaje de escombros, su efectividad técnica, económica, y el impacto social y ecológico que proporciona a la sociedad, es nuestro punto de partida para lograr un óptimo aprovechamiento de este árido como futuro agregado fundamental en la obtención de un mortero de albañilería, capaz de tener como propiedades aquellas intrínsecas de los propios morteros obtenidos a partir de áridos de cantera y recogidos en la norma cubana NC52-79:93. El trabajo consiste en la preparación y estudio de morteros de albañilería empleando árido reciclado -producto de demolición- como agregado. Se prepararon 4 dosificaciones volumétricas (1:4; 1:5; 1:6 y 1:8), las cuales fueron sometidas a ensayos físico-mecánicos al, 28 y 60 días, resistencia a la adherencia a 28 días, y absorción capilar, obteniéndose resultados comparables con los morteros de albañilería tradicionales

Chiral Symmetry and light resonances in hot and dense matter

We present a study of the $\pi\pi$ scattering amplitude in the $\sigma$ and $\rho$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar-isoscalar channel to account for finite nuclear density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear matter and Heavy-Ion Collision experiments, such as $\rho$ mass scaling vs broadening from dilepton spectra and chiral restoration signals in the $\sigma$ channel. We also elaborate on the molecular nature of $\pi\pi$ resonances.Comment: 14 pages, 14 figures. Contribution to Hard Probes 2008, Illa de A Toxa, Spain, June 8th-14th 200