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 $w\geq 0$. We name it {\it distorted Heisenberg algebra}, where $w$ is the distortion parameter. The corresponding coherent states for an arbitrary $w$ 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

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

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

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$_3$, 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 $n$-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