44,798 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
Reference priors in non-normal location problems
Bayesian Statistics;Statistical Distribution
Multivariate Student -t Regression Models: Pitfalls and Inference
We consider likelihood-based inference from multivariate regression models with independent Student-t errors. Some very intruiging pitfalls of both Bayesian and classical methods on the basis of point observations are uncovered. Bayesian inference may be precluded as a consequence of the coarse nature of the data. Global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space. A Bayesian analysis on the basis of set observations is proposed and illustrated by several examples.Bayesian inference;Coarse data;Continuous distribution;Maximum likelihood;Missing data;Scale mixture of Normals
Geometric Phases and Mielnik's Evolution Loops
The cyclic evolutions and associated geometric phases induced by
time-independent Hamiltonians are studied for the case when the evolution
operator becomes the identity (those processes are called {\it evolution
loops}). We make a detailed treatment of systems having equally-spaced energy
levels. Special emphasis is made on the potentials which have the same spectrum
as the harmonic oscillator potential (the generalized oscillator potentials)
and on their recently found coherent states.Comment: 11 pages, harvmac, 2 figures available upon request; CINVESTAV-FIS
GFMR 11/9
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
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