Overcritical PT-symmetric square well potential in the Dirac equation

We study scattering properties of a PT-symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the (1+1)-dimensional Dirac equation.Comment: 11 pages, 1 figure, to appear in Physics Letters

On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass

The relativistic problem of fermions subject to a PT-symmetric potential in the presence of position-dependent mass is reinvestigated. The influence of the PT-symmetric potential in the continuity equation and in the orthonormalization condition are analyzed. In addition, a misconception diffused in the literature on the interaction of neutral fermions is clarified.Comment: 8 page

Green Functions for the Wrong-Sign Quartic

It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric explicitly, by truncation of the equations. Such a calculation has recently been carried out for various $PT$-symmetric theories, in both quantum mechanics and quantum field theory, including the wrong-sign quartic oscillator. For this particular theory the metric is known in closed form, making possible an independent check of these approximate results. We do so by numerically evaluating the ground-state wave-function for the equivalent Hermitian Hamiltonian and using this wave-function, in conjunction with the metric operator, to calculate the one- and two-point Green functions. We find that the Green functions evaluated by lowest-order truncation of the Schwinger-Dyson equations are already accurate at the (6-8)% level. This provides a strong justification for the method and a motivation for its extension to higher order and to higher dimensions, where the calculation of the metric is extremely difficult

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

A 60 pc counter-rotating core in NGC 4621

We present adaptive optics assisted OASIS integral field spectrography of the S0 galaxy NGC 4621. Two-dimensional stellar kinematical maps (mean velocity and dispersion) reveal the presence of a 60 pc diameter counter-rotating core (CRC), the smallest observed to date. The OASIS data also suggests that the kinematic center of the CRC is slightly offset from the center of the outer isophotes. This seems to be confirmed by archival HST/STIS data. We also present the HST/WFPC2 V-I colour map, which exhibits a central elongated red structure, also slightly off-centered in the same direction as the kinematic centre. We then construct an axisymmetric model of NGC 4621: the two-integral distribution function is derived using the Multi-Gaussian Expansion and the Hunter & Qian (1993) formalisms. Although the stellar velocities are reasonably fitted, including the region of the counter-rotating core, significant discrepancies between the model and the observations demonstrate the need for a more general model (e.g. a three-integral model).Comment: 9 pages, 8 figure

Time-Reversal Violating Schiff Moment of 225Ra

We use the Skyrme-Hartree-Fock method, allowing all symmetries to be broken, to calculate the time-reversal-violating nuclear Schiff moment (which induces atomic electric dipole moments) in the octupole-deformed nucleus 225Ra. Our calculation includes several effects neglected in earlier work, including self consistency and polarization of the core by the last nucleon. We confirm that the Schiff moment is large compared to those of reflection-symmetric nuclei, though ours is generally a few times smaller than recent estimates.Comment: Typos corrected, references added, minor changesin text. Version to appear in PRC. 10 pages, 4 figure

Evidence of a distinct stellar population in the counter-rotating core of NGC 1700

We find a distinct stellar population in the counter-rotating and kinematically decoupled core of the isolated massive elliptical galaxy NGC 1700. Coinciding with the edge of this core we find a significant change in the slope of the gradient of various representative absorption line indices. Our age estimate for this core is markedly younger than the main body of the galaxy. We find lower values for the age, metallicity and Mg/Fe abundance ratio in the center of this galaxy when we compare them with other isolated elliptical galaxies with similar velocity dispersion. We discuss the different possible scenarios that might have lead to the formation of this younger kinematically decoupled structure and conclude that, in light of our findings, the ingestion of a small stellar companion on a retrograde orbit is the most favoured.Comment: 13 pages, 5 figures, accepted for publication in ApJ

Sherrington-Kirkpatrick model near T=TcT=T_c: expanding around the Replica Symmetric Solution

An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} = \delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the expansion is truncated to fourth order in. $Q_{ab} - Q^{({\rm RS})}_{ab}$. The Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns out to exist only in the range of temperature $0.549...\leq T\leq T_c=1$, not including T=0. On the other hand an expansion around the paramagnetic solution $Q^{({\rm PM})}_{ab} = \delta_{ab}$ up to fourth order yields a FRSB solution that exists in a limited temperature range $0.915...\leq T \leq T_c=1$.Comment: 18 pages, 3 figure

Stellar Absorption Lines in the Spectra of Seyfert Galaxies

We have measured the strengths of Ca II Triplet and Mgb stellar absorption lines in the nuclear and off-nuclear spectra of Seyfert galaxies. These features are diluted to varying degrees by continuum emission from the active nucleus and from young stars. Ca II Triplet strengths can be enhanced if late-type supergiant stars dominate the near-IR light. Thus, objects with strong Ca II Triplet and weak Mgb lines may be objects with strong bursts of star formation. We find that for most of our sample the line strengths are at least consistent with dilution of a normal galaxy spectrum by a power law continuum, in accord with the standard model for AGN. However, for several Seyferts in our sample, it appears that dilution by a power law continuum cannot simultaneously explain strong Ca II Triplet and relatively weak Mgb. Also, these objects occupy the region of the IRAS color-color diagram characteristic of starburst galaxies. In these objects it appears that the optical to near-IR emission is dominated by late-type supergiants produced in a circumnuclear burst of star formation.Comment: 4 pages, 3 figures, to appear in Advances in Space Research, presented at "The AGN/Host Galaxy Connection" as part of the Scientific Assembly of COSPAR, July 12-18 Nagoya, Japa