Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetry

The kinetic energy operator with position-dependent-mass in cylindrical coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed within radial cylindrical mass settings. Azimuthal symmetry is assumed and spectral signatures of various z-dependent interaction potentials (Hermitian and non-Hermitian PT-symmetric) are reported.Comment: 16 page

The neonatal splice variant of Nav1.5 potentiates in vitro invasive behaviour of MDA-MB-231 human breast cancer cells

Upregulation of functional voltage-gated Na+ channels (VGSCs) occurs in metastatic human breast cancer (BCa) in vitro and in vivo. The present study aimed to ascertain the specific involvement of the 'neonatal' splice variant of Nav1.5 (nNav1.5), thought to be predominant, in the VGSC-dependent invasive behaviour of MDA-MB-231 cells. Functional activity of nNav1.5 was suppressed by two different methods targeting nNav1.5: (i) small interfering RNA (siRNA), and (ii) a polyclonal antibody (NESO-pAb); effects upon migration and invasion were determined. nNav1.5 mRNA, protein and signalling were measured using real-time PCR, Western blotting, and patch clamp recording, respectively. Treatment with the siRNA rapidly reduced (by similar to 90%) the level of nNav1.5 (but not adult Nav1.5) mRNA, but the protein reduction was much smaller (similar to 30%), even after 13 days. Nevertheless, the siRNA reduced peak VGSC current density by 33%, and significantly increased the cells' sensitivity to nanomolar tetrodotoxin (TTX). Importantly, the siRNA suppressed in vitro migration by 43%, and eliminated the normally inhibitory effect of TTX. Migrated MDA-MB-231 cells expressed more nNav1.5 protein at the plasma membrane than non-migrated cells. Furthermore, NESO-pAb reduced migration by up to 42%, in a dose-dependent manner. NESO-pAb also reduced Matrigel invasion without affecting proliferation. TTX had no effect on cells already treated with NESO-pAb. It was concluded that nNav1.5 is primarily responsible for the VGSC-dependent enhancement of invasive behaviour in MDA-MB-231 cells. Accordingly, targeting nNav1.5 expression/activity may be useful in clinical management of metastatic BCa

Nerve growth factor enhances voltage-gated Na+ channel activity and transwell migration in Mat-LyLu rat prostate cancer cell line

The highly dynamic nature of voltage-gated Na+ channel (VGSC) expression and its controlling mechanism(s) are not well understood. In this study, we investigated the possible involvement of nerve growth factor (NGF) in regulating VGSC activity in the strongly metastatic Mat-LyLu cell model of rat prostate cancer (PCa). NGF increased peak VGSC current density in a time- and dose-dependent manner. NGF also shifted voltage to peak and the half-activation voltage to more positive potentials, and produced currents with faster kinetics of activation; sensitivity to the VGSC blocker tetrodotoxin (TTX) was not affected. The NGF-induced increase in peak VGSC current density was suppressed by both the pan-trk antagonist K252a, and the protein kinase A (PKA) inhibitor KT5720. NGF did not affect the Nav1.7 mRNA level, but the total VGSC alpha-subunit protein level was upregulated. NGF potentiated the cells' migration in Transwell assays, and this was not affected by TTX. We concluded that NGF upregulated functional VGSC expression in Mat-LyLu cells, with PKA as a signaling intermediate, but enhancement of migration by NGF was independent of VGSC activity

On the Explanation of the Paramagnetic Meissner Effect in Superconductor/Ferromagnet Heterostructures

An increase of the magnetic moment in superconductor/ferromagnet (S/F) bilayers V(40nm)/F [F$=$Fe(1,3nm), Co(3nm), Ni(3nm)] was observed using SQUID magnetometry upon cooling below the superconducting transition temperature Tc in magnetic fields of 10 Oe to 50 Oe applied parallel to the sample surface. A similar increase, often called the paramagnetic Meissner effect (PME), was observed before in various superconductors and superconductor/ferromagnet systems. To explain the PME effect in the presented S/F bilayers a model based on a row of vortices located at the S/F interface is proposed. According to the model the magnetic moment induced below Tc consists of the paramagnetic contribution of the vortex cores and the diamagnetic contribution of the vortex-free region of the S layer. Since the thickness of the S layer is found to be 3-4 times less than the magnetic field penetration depth, this latter diamagnetic contribution is negligible. The model correctly accounts for the sign, the approximate magnitude and the field dependence of the paramagnetic and the Meissner contributions of the induced magnetic moment upon passing the superconducting transition of a ferromagnet/superconductor bilayer

Pseudoduality Between Symmetric Space Sigma Models

We study the pseudoduality transformation on the symmetric space sigma models. We switch the Lie group valued pseudoduality equations to Lie algebra valued ones, which leads to an infinite number of pseudoduality equations. We obtain an infinite number of conserved currents on the tangent bundle of the pseudodual manifold. We show that there can be mixing of decomposed spaces with each other, which leads to mixings of the following expressions. We obtain the mixing forms of curvature relations and one loop renormalization group beta functions by means of these currents.Comment: 33 pages, typos corrected and some new references adde

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in J.Phys.A (Fast Track Communication

Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential

The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.Comment: 10 page

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge