21,855 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
Supersymmetric partners of the trigonometric Poschl-Teller potentials
The first and second-order supersymmetry transformations are used to generate
Hamiltonians with known spectra departing from the trigonometric Poschl-Teller
potentials. The several possibilities of manipulating the initial spectrum are
fully explored, and it is shown how to modify one or two levels, or even to
leave the spectrum unaffected. The behavior of the new potentials at the
boundaries of the domain is studied.Comment: 20 pages, 4 figure
Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians
The dynamical algebra associated to a family of isospectral oscillator
Hamiltonians is studied through the analysis of its representation in the basis
of energy eigenstates. It is shown that this representation becomes similar to
that of the standard Heisenberg algebra, and it is dependent of a parameter
. We name it {\it distorted Heisenberg algebra}, where is the
distortion parameter. The corresponding coherent states for an arbitrary
are derived, and some particular examples are discussed in full detail. A
prescription to produce the squeezing, by adequately selecting the initial
state of the system, is given.Comment: 21 pages, Latex, 3 figures available as hard copies upon request from
the first Autho
Berry phase in homogeneous K\"ahler manifolds with linear Hamiltonians
We study the total (dynamical plus geometrical (Berry)) phase of cyclic
quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H,
which can be considered as the phase spaces of classical systems and which are,
in particular cases, coadjoint orbits of some Lie groups G. When the
Hamiltonian is linear in the generators of a Lie group, both phases can be
calculated exactly in terms of {\em classical} objects. In particular, the
geometric phase is given by the symplectic area enclosed by the (purely
classical) motion in the space of coherent states.Comment: LaTeX fil
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
Quantum mechanical spectral engineering by scaling intertwining
Using the concept of spectral engineering we explore the possibilities of
building potentials with prescribed spectra offered by a modified intertwining
technique involving operators which are the product of a standard first-order
intertwiner and a unitary scaling. In the same context we study the iterations
of such transformations finding that the scaling intertwining provides a
different and richer mechanism in designing quantum spectra with respect to
that given by the standard intertwiningComment: 8 twocolumn pages, 5 figure
Van der Waals spin valves
We propose spin valves where a 2D non-magnetic conductor is intercalated
between two ferromagnetic insulating layers. In this setup, the relative
orientation of the magnetizations of the insulating layers can have a strong
impact on the in-plane conductivity of the 2D conductor. We first show this for
a graphene bilayer, described with a tight-binding model, placed between two
ferromagnetic insulators. In the anti-parallel configuration, a band gap opens
at the Dirac point, whereas in the parallel configuration, the graphene bilayer
remains conducting. We then compute the electronic structure of graphene
bilayer placed between two monolayers of the ferromagnetic insulator CrI,
using density functional theory. Consistent with the model, we find that a gap
opens at the Dirac point only in the antiparallel configuration.Comment: 5 pages, 4 figure
Second Order Darboux Displacements
The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived
Exactly Solvable Hydrogen-like Potentials and Factorization Method
A set of factorization energies is introduced, giving rise to a
generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for
the radial hydrogen-like Hamiltonian. An algebraic intertwining technique
involving such factorization energies leads to derive -parametric families
of potentials in general almost-isospectral to the hydrogen-like radial
Hamiltonians. The construction of SUSY partner Hamiltonians with ground state
energies greater than the corresponding ground state energy of the initial
Hamiltonian is also explicitly performed.Comment: LaTex file, 21 pages, 2 PostScript figures and some references added.
To be published in J. Phys. A: Math. Gen. (1998
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