43,088 research outputs found
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
Trends in Supersymmetric Quantum Mechanics
Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two Hamiltonians through a finite order differential operator. Some related subjects can be simply analyzed, as the algebras ruling both Hamiltonians and the associated coherent states. The technique has been applied also to periodic potentials, where the spectra consist of allowed and forbidden energy bands. In addition, a link with non-linear second-order differential equations, and the possibility of generating some solutions, can be explored. Recent applications concern the study of Dirac electrons in graphene placed either in electric or magnetic fields, and the analysis of optical systems whose relevant equations are the same as those of SUSY QM. These issues will be reviewed briefly in this paper, trying to identify the most important subjects explored currently in the literature
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
Supersymmetric quantum mechanics and Painleve equations
In these lecture notes we shall study first the supersymmetric quantum
mechanics (SUSY QM), specially when applied to the harmonic and radial
oscillators. In addition, we will define the polynomial Heisenberg algebras
(PHA), and we will study the general systems ruled by them: for zero and first
order we obtain the harmonic and radial oscillators, respectively; for second
and third order PHA the potential is determined by solutions to Painleve IV
(PIV) and Painleve V (PV) equations. Taking advantage of this connection, later
on we will find solutions to PIV and PV equations expressed in terms of
confluent hypergeometric functions. Furthermore, we will classify them into
several solution hierarchies, according to the specific special functions they
are connected with.Comment: 38 pages, 20 figures. Lecture presented at the XLIII Latin American
School of Physics: ELAF 2013 in Mexico Cit
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