Is there a prescribed parameter's space for the adiabatic geometric phase?

The Aharonov-Anandan and Berry phases are determined for the cyclic motions of a non-relativistic charged spinless particle evolving in the superposition of the fields produced by a Penning trap and a rotating magnetic field. Discussion about the selection of the parameter's space and the relationship between the Berry phase and the symmetry of the binding potential is given.Comment: 7 pages, 2 figure

Harmonic Oscillator SUSY Partners and Evolution Loops

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied

Is the bulbus arteriosus of fish homologous to the mamalian intrapericardial thoracic arteries?

El resumen aparece en el Program & Abstracts of the 10th International Congress of Vertebrate Morphology, Barcelona 2013.Anatomical Record, Volume 296, Special Feature — 1: P-089.Two major findings have significantly improved our understanding of the embryology and evolution of the arterial pole of the vertebrate heart (APVH): 1) a new embryonic presumptive cardiac tissue, named second heart field (SHF), forms the myocardium of the outflow tract, and the walls of the ascending aorta (AA) and the pulmonary trunk (PT) in mammals and birds; 2) the bulbus arteriosus (BA), previously thought to be an actinopterygian apomorphy, is present in all basal Vertebrates, and probably derives from the SHF. We hypothesized that the intrapericardial portions of the AA and the PT of mammals are homologous to the BA of basal vertebrates. To test this, we performed 1) a literature review of the anatomy and embryology of the APVH; 2) novel anatomical, histomorphological, and embryological analyses of the APVH, comparing basal (Galeus atlanticus), with apical (Mus musculus and Mesocricetus auratus) vertrebrates. Evidence obtained: 1) Anatomically, BA, AA, and PT are muscular tubes into the pericardial cavity, which connect the distal myocardial outflow tracts with the aortic arch system. Coronary arteries run through or originate at these anatomical structures; 2) Histologically, BA, AA, and PT show an inner layer of endothelium covered by circumferentially oriented smooth muscle cells, collagen fibers, and lamellar elastin. The histomorphological differences between the BA and the ventral aorta parallel those between intrapericardial and extrapericardial great arteries; 3) Embryologically, BA, AA, and PT are composed of smooth muscle cells derived from the SHF. They show a similar mechanism of development: incorporation of SHF‐derived cells into the pericardial cavity, and distal‐to‐proximal differentiation into an elastogenic cell linage. In conclusion, anatomical, histological and embryological evidence supports the hypothesis that SHF is a developmental unit responsible for the formation of the APVH. The BA and the intrapericardial portions of the great arteries must be considered homologous structures.Proyecto P10-CTS-6068 (Junta de Andalucía); proyecto CGL-16417 (Ministerio de Ciencia e Innovación); Fondos FEDER

Wronskian formula for confluent second-order supersymmetric quantum mechanics

The confluent second-order supersymmetric quantum mechanics, for which the factorization energies tend to a single value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed solutions. The confluent algorithm is used to generate SUSY partners of the Coulomb potential.Comment: 7 pages, 1 figure, to be published in Physics Letters

Supersymmetric Quantum Mechanics and Painlev\'e IV Equation

As it has been proven, the determination of general one-dimensional Schr\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\'e IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlev\'e IV equation. Finally, we classify these solutions into three relevant hierarchies.Comment: Proceedings of the Workshop 'Supersymmetric Quantum Mechanics and Spectral Design' (July 18-30, 2010, Benasque, Spain