Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

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

On the hereditary character of new strong variations of weyl type theorems

Berkani and Kachad [18], [19], and Sanabria et al. [32], introduced and studied strong variations of Weyl type Theorems. In this paper, we study the behavior of these strong variations of Weyl type theorems for an operator T on a proper closed and Tinvariant subspace W ⊆ X such that T n (X) ⊆ W for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. The main purpose of this paper is to prove that for these subspaces (which generalize the case T n (X) closed for some n ≥ 0), these strong variations of Weyl type theorems are preserved from T to its restriction on W and vice-versa. As consequence of our results, we give sufficient conditions for which these strong variations of Weyl type Theorems are equivalent for two given operators. Also, some applications to multiplication operators acting on the boundary variation space BV [0, 1] are given

A note on preservation of generalized fredholm spectra in berkani’s sense

In this paper, we study the relationships between the spectra derived from B-Fredholm theory corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral properties corresponding to two given operators are the same. As application of our results, we obtain conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm theory are the same

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

Temperature effects on sinking velocity of different Emiliania huxleyi strains

The sinking properties of three strains of Emiliania huxleyi in response to temperature changes were examined. We used a recently proposed approach to calculate sinking velocities from coccosphere architecture, which has the advantage to be applicable not only to culture samples, but also to field samples including fossil material. Our data show that temperature in the sub-optimal range impacts sinking velocity of E. huxleyi. This response is widespread among strains isolated in different locations and moreover comparatively predictable, as indicated by the similar slopes of the linear regressions. Sinking velocity was positively correlated to temperature as well as individual cell PIC/POC over the sub-optimum to optimum temperature range in all strains. In the context of climate change our data point to an important influence of global warming on sinking velocities. It has recently been shown that seawater acidification has no effect on sinking velocity of a Mediterranean E. huxleyi strain, while nutrient limitation seems to have a small negative effect on sinking velocity. Given that warming, acidification, and lowered nutrient availability will occur simultaneously under climate change scenarios, the question is what the net effect of different influential factors will be. For example, will the effects of warming and nutrient limitation cancel? This question cannot be answered conclusively but analyses of field samples in addition to laboratory culture studies will improve predictions because in field samples multi factor influences and even evolutionary changes are not excluded. As mentioned above, the approach of determining sinking rate followed here is applicable to field samples. Future studies could use it to analyse not only seasonal and geographic patterns but also changes in sinking velocity over geological time scales

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

The supersymmetric modified Poschl-Teller and delta-well potentials

New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values of the parameters for which these potentials are free of singularities is exactly determined. The construction of higher order supersymmetric partner potentials is also investigated.Comment: 20 pages, LaTeX file, 4 eps figure

Optimizing Fully Anisotropic Elastic Propagation on 2nd Generation Intel Xeon Phi Processors

This work shows several optimization strategies evaluated and applied to an elastic wave propagation engine, based on a Fully Staggered Grid, running on the latest Intel Xeon Phi processors, the second generation of the product (code-named Knights Landing). Our fully optimized code shows a speed-up of about 4x when compared with the same algorithm optimized for the previous generation processor.Authors also thank Repsol for the permission to publish the present research, carried out at the Repsol-BSC Research Center. This work has received funding from the European Union's Horizon 2020 Programme (2014-2020) and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP) under the HPC4E Project (www.hpc4e.eu), grant agreement n.◦ 689772. * Other brands and names are the property of their respective owners.Peer ReviewedPostprint (author's final draft