Non-Hermitian von Roos Hamiltonian's η\eta-weak-pseudo-Hermiticity, isospectrality and exact solvability

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables, the $\eta$-weak-pseudo-Hermitian von Roos Hamiltonians H(x) are mapped into the traditional Schrodinger Hamiltonian form H(q), where exact isospectral correspondence between H(x) and H(q) is obtained. Under a user-friendly position dependent mass settings, it is observed that for each exactly-solvable $\eta$-weak-pseudo-Hermitian reference-Hamiltonian H(q)there is a set of exactly-solvable $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians H(x). A non-Hermitian PT-symmetric Scarf II and a non-Hermitian periodic-type PT-symmetric Samsonov-Roy potentials are used as reference models and the corresponding $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.Comment: 11 pages, no figures

The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for $n=2-10$ and $m=0-1$ states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.Comment: 13 pages and 5 table

Are there plasminos in superconductors?

Hot and/or dense, normal-conducting systems of relativistic fermions exhibit a particular collective excitation, the so-called plasmino. We compute the one-loop self-energy, the dispersion relation and the spectral density for fermions interacting via attractive boson exchange. It is shown that plasminos also exist in superconductors.Comment: 15 pages, 14 figures, revte

Can Van Hove singularities be observed in relativistic heavy-ion collisions ?

Based on general arguments the in-medium quark propagator in a quark-gluon plasma leads to a quark dispersion relation consisting of two branches, of which one exhibits a minimum at some finite momentum. This results in a vanishing group velocity for collective quark modes. Important quantities such as the production rate of low mass lepton pairs and mesonic correlators depend inversely on this group velocity. Therefore these quantities, which follow from self energy diagrams containing a quark loop, are strongly affected by Van Hove singularities (peaks and gaps). If these sharp structures could be observed in relativistic heavy-ion collisions it would reveal the physical picture of the QGP as a gas of quasiparticles.Comment: 12 pages including nine figures and style files, invited talk given at the ICPAQGP-2001, November 26-30, 2001, Jaipur, Indi

(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib) (an inversely linear plus linear, leading to a PT-symmetric oscillator model), and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an $\eta$-weak-pseudo-Hermiticity generator are presented and a complexified PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise

Evidence for spin-triplet superconducting correlations in metal-oxide heterostructures with non-collinear magnetization

Heterostructures composed of ferromagnetic La0.7Sr0.3MnO3, ferromagnetic SrRuO3, and superconducting YBa2Cu3Ox were studied experimentally. Structures of composition Au/La0.7Sr0.3MnO3/SrRuO3/YBa2Cu3Ox were prepared by pulsed laser deposition, and their high quality was confirmed by X-ray diffraction and reflectometry. A non-collinear magnetic state of the heterostructures was revealed by means of SQUID magnetometry and polarized neutron reflectometry. We have further observed superconducting currents in mesa-structures fabricated by deposition of a second superconducting Nb layer on top of the heterostructure, followed by patterning with photolithography and ion-beam etching. Josephson effects observed in these mesa-structures can be explained by the penetration of a triplet component of the superconducting order parameter into the magnetic layers.Comment: 10 pages, 6 figure

Unidirectional Invisibility and PT-Symmetry with Graphene

We investigate the reflectionlessness and invisibility properties in the transverse electric (TE) mode solution of a linear homogeneous optical system which comprises the $\mathcal{PT}$-symmetric structures covered by graphene sheets. We derive analytic expressions, indicate roles of each parameter governing optical system with graphene and justify that optimal conditions of these parameters give rise to broadband and wide angle invisibility. Presence of graphene turns out to shift the invisible wavelength range and to reduce the required gain amount considerably, based on its chemical potential and temperature. We substantiate that our results yield broadband reflectionless and invisible configurations for realistic materials of small refractive indices, usually around $\eta = 1$, and of small thickness sizes with graphene sheets of rather small temperatures and chemical potentials. Finally, we demonstrate that pure $\mathcal{PT}$-symmetric graphene yields invisibility at small temperatures and chemical potentials.Comment: 20 pages, 1 table 17 figure

First-order intertwining operators with position dependent mass and η\eta- weak-psuedo-Hermiticity generators

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target $\eta$-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some $\eta$-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding $\eta$-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are given as products of the reference-target map.Comment: 11 pages, no figures, Revised/Expanded, more references added. To appear in the Int.J. Theor. Phy

Effect of vitamin A and undernutrition on the susceptibility of rodents to a malarial parasite Plasmodium berghei

The ability of vitamin A deficient rats to resist infection with P. berghei was investigated. When 10×106 erythrocytes bearing the parasite/100 g body weight were given to the vitamin A protein energy undernourished rats, parasitemia developed in these animals at a faster pace than the controls. A high number (60% to 95% ) of red blood cells (RBC) carrying the parasite were noticeable within 6 to 7 days after infection, at which time most animals in this group died. The pair-fed controls (protein-energy undernourished but supplemented with vitamin A) fared perceptibly better with an equivalent load of infection. Control ad libitum fed littermates were able to restrict the infection and neither high parasitemia nor death was noted in this group. Oral supplements of retinyl acetate to vitamin A deficient rats enabled the animals to recover from infection. A subclinical dose of 500 parasitized RBC given at an early stage of the vitamin A deficiency precipitated the deficiency symptoms at a faster rate and led to the development of higher order of parasitemia in these rats beginning from the 10th day after infection as compared to pair fed controls. The yield of glass adhering cells obtainable from peritoneal exudates was low in deficient rats. In vitro experiments further suggest a decrease in the capacity of the glass adhering peritoneal exudate cells in vitamin A deficient mice to clear the infection. This capacity was improved by addition of non glass adhering cells from sensitized control mice