Conditionally Exactly Solvable Potentials and Supersymmetric Transformations

A general procedure is presented to construct conditionally solvable (CES) potentials using the techniques of supersymmetric quantum mechanics.The method is illustrated with potentials related to the harmonic oscillator problem.Besides recovering known results,new CES potentials are also obtained within the framework of this general approach.The conditions under which this method leads to CES potentials are also discussed.Comment: 10 pages,Reference adde

PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential

Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in general. Some aspects of the spontaneous breakdown of PT symmetry are analysed.Comment: 16 pages; to appear in Phys. lett.

Chiral Magnetic Effect in the Dirac-Heisenberg-Wigner formalism

In this paper the emergence of the Chiral Magnetic Effect (CME) and the related anomalous current is investigated using the real time Dirac-Heisenberg-Wigner formalism. This method is widely used for describing strong field physics and QED vacuum tunneling phenomena as well as pair production in heavy-ion collisions. We extend earlier investigations of the CME in constant flux tube configuration by considering time dependent fields. In this model we can follow the formation of axial charge separation, formation of axial current and then the emergence of the anomalous electric current. Qualitative results are shown for special field configurations that help to interpret the predictions of CME related effects in heavy-ion collisions at the RHIC Beam Energy Scan program.Comment: 5 pages, 5 figure

Scattering in the PT-symmetric Coulomb potential

Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions valid for non-integer values of the 2L parameter, which would correspond to the angular momentum in the usual Hermitian setting. Transmission and reflection coefficients are written in closed analytic form and it is shown that similarly to other ${\cal PT}$-symmetric scattering systems the latter exhibit handedness effect. Bound-state energies are recovered from the poles of the transmission coefficients.Comment: Journal of Physics A: Mathematical and Theoretical 42 (2009) to appea

Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'

We demonstrate that the recent paper by Abhinav and Panigrahi entitled `Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex $sl(2)$ potential algebra.Comment: 6 pages, no figure, published versio

Exact solutions of the sextic oscillator from the bi-confluent Heun equation

The sextic oscillator is discussed as a potential obtained from the bi-confluent Heun equation after a suitable variable transformation. Following earlier results, the solutions of this differential equation are expressed as a series expansion of Hermite functions with shifted and scaled arguments. The expansion coefficients are obtained from a three-term recurrence relation. It is shown that this construction leads to the known quasi-exactly solvable form of the sextic oscillator when some parameters are chosen in a specific way. By forcing the termination of the recurrence relation, the Hermite functions turn into Hermite polynomials with shifted arguments, and, at the same time, a polynomial expression is obtained for one of the parameters, the roots of which supply the energy eigenvalues. With the $\delta=0$ choice the quartic potential term is cancelled, leading to the {\it reduced} sextic oscillator. It was found that the expressions for the energy eigenvalues and the corresponding wave functions of this potential agree with those obtained from the quasi-exactly solvable formalism. Possible generalizations of the method are also presented

Schroedinger equations with indefinite effective mass

The consistency of the concept of quantum (quasi)particles possessing effective mass which is both position- and excitation-dependent is analyzed via simplified models. It is shown that the system may be stable even when the effective mass m=m(x,E) itself acquires negative values in a limited range of coordinates x and energies E.Comment: 17 pp., 3 fig

Simulation of Pair Production in Extreme Strong EM Fields

In this article we review a theoretical framework for pair production from strong external electromagnetic fields. We propose a numerical method to solve the resulting equations of motion and present results for both cases of spatially homogeneous and inhomogeneous electric fields.Comment: 5 pages, 2 figure

The production of charm mesons from quark matter at CERN SPS and RHIC

We study the production of charm mesons and other charm baryons from quark matter at CERN SPS and RHIC energies. Using quark coalescence models as hadronization mechanism, we predict particle ratios, absolute yields and transverse momentum spectra.Comment: 4 pages in Latex, 2 PS figure, to be published in the proceedings of the SQM'2000 Conference, Berkeley, CA, July 20-25, 2000. Submitted to J. Phys.

The Nuclear Modification Factor at Large Rapidities

RHIC data on high-$p_T$ hadron production display strong suppression in a wide rapidity region, indicating strong induced energy loss for both transversally and longitudinally traveling partons. We investigate the interplay of energy loss and rapidity dependence in a perturbative QCD improved parton model, and estimate the opacity of the produced hot matter in $AuAu$ collisions at energies $\sqrt{s}=200$ $A$GeV and 63 $A$GeV at different rapidity values. Direction-dependent suppression offers the possibility to study the geometry of the hot matter.Comment: 4 pages, 2 figures, Contribution to the Poster Proceedings of the Quark Matter 2005 Conference. To be published in Nuclear Physics