1,538 research outputs found
New features of scattering from a one-dimensional non-Hermitian (complex) potential
For complex one-dimensional potentials, we propose the asymmetry of both
reflectivity and transmitivity under time-reversal: and , unless the potentials are real or PT-symmetric. For complex
PT-symmetric scattering potentials, we propose that
and . So far, the spectral singularities (SS) of a one-dimensional
non-Hermitian scattering potential are witnessed/conjectured to be at most one.
We present a new non-Hermitian parametrization of Scarf II potential to reveal
its four new features. Firstly, it displays the just acclaimed (in)variances.
Secondly, it can support two spectral singularities at two pre-assigned real
energies () either in or in , when
. Thirdly, when it possesses one SS in
and the other in . Fourthly, when the potential becomes PT-symmetric
, we get , it possesses a unique SS at
in both and . Lastly, for completeness, when
and , there are no SS, instead we get two
negative energies and of the complex PT-symmetric Scarf
II belonging to the two well-known branches of discrete bound state eigenvalues
and no spectral singularity exists in this case. We find them as
and ; with
.
{PACS: 03.65.Nk,11.30.Er,42.25.Bs}Comment: 10 pages, one Table, one Figure, important changes, appeared as an
FTC (J. Phys. A: Math. Theor. 45(2012) 032004
Is Strangeness Still Strange at the LHC?
Strangeness production is calculated in a pQCD-based model (including nuclear
effects) in the high transverse momentum sector, where pQCD is expected to work
well. We investigate pion, kaon, proton and lambda production in pp and
heavy-ion collisions. Parton energy loss in AA collisions is taken into
account. We compare strange-to-non-strange meson and baryon ratios to data at
RHIC, and make predictions for the LHC. We find that these ratios significantly
deviate from unity not only at RHIC but also at the LHC, indicating the special
role of strangeness at both energies.Comment: Contribution to SQM 2007, 6 pages 2 figure
Breaking so(4) symmetry without degeneracy lift
We argue that in the quantum motion of a scalar particle of mass "m" on S^3_R
perturbed by the trigonometric Scarf potential (Scarf I) with one internal
quantized dimensionless parameter, \ell, the 3D orbital angular momentum, and
another, an external scale introducing continuous parameter, B, a loss of the
geometric hyper-spherical so(4) symmetry of the free motion can occur that
leaves intact the unperturbed {\mathcal N}^2-fold degeneracy patterns, with
{\mathcal N}=(\ell +n+1) and n denoting the nodes number of the wave function.
Our point is that although the number of degenerate states for any {\mathcal N}
matches dimensionality of an irreducible so(4) representation space, the
corresponding set of wave functions do not transform irreducibly under any
so(4). Indeed, in expanding the Scarf I wave functions in the basis of properly
identified so(4) representation functions, we find power series in the
perturbation parameter, B, where 4D angular momenta K\in [\ell , {\mathcal
N}-1] contribute up to the order \left(\frac{2mR^2B}{\hbar^2}\right)^{{\mathcal
N}-1-K}. In this fashion, we work out an explicit example on a symmetry
breakdown by external scales that retains the degeneracy. The scheme extends to
so(d+2) for any d.Comment: Prepared for the proceedings of the conference "Lie Theory and Its
Applications In Physics", June 17-23, 2013, Varna, Bulgari
Method for Generating Additive Shape Invariant Potentials from an Euler Equation
In the supersymmetric quantum mechanics formalism, the shape invariance
condition provides a sufficient constraint to make a quantum mechanical problem
solvable; i.e., we can determine its eigenvalues and eigenfunctions
algebraically. Since shape invariance relates superpotentials and their
derivatives at two different values of the parameter , it is a non-local
condition in the coordinate-parameter space. We transform the shape
invariance condition for additive shape invariant superpotentials into two
local partial differential equations. One of these equations is equivalent to
the one-dimensional Euler equation expressing momentum conservation for
inviscid fluid flow. The second equation provides the constraint that helps us
determine unique solutions. We solve these equations to generate the set of all
known -independent shape invariant superpotentials and show that there
are no others. We then develop an algorithm for generating additive shape
invariant superpotentials including those that depend on explicitly,
and derive a new -dependent superpotential by expanding a Scarf
superpotential.Comment: 1 figure, 4 tables, 18 page
Pauli equation and the method of supersymmetric factorization
We consider different variants of factorization of a 2x2 matrix
Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its
spectrum to the sum of spectra of two scalar Schroedinger operators, in a
manner similar to one-dimensional Darboux transformations. We consider both the
case when such factorization is reduced to the ordinary 2-dimensional SUSY QM
quasifactorization and a more general case which involves covariant
derivatives. The admissible classes of electromagnetic fields are described and
some illustrative examples are given.Comment: 18 pages, Late
Probing the QCD Equation of State
We propose a novel quasiparticle interpretation of the equation of state of
deconfined QCD at finite temperature. Using appropriate thermal masses, we
introduce a phenomenological parametrisation of the onset of confinement in the
vicinity of the phase transition. Lattice results of bulk thermodynamic
quantities are well reproduced, the extension to small quark chemical potential
is also successful. We then apply the model to dilepton production and charm
suppression in ultrarelativistic heavy-ion collisions.Comment: 6 pages, 8 figures. Invited talk presented by R. A. Schneider at the
XVI International Conference on Particles and Nuclei (PANIC02), Osaka, Japan,
September 30 - October 4, 200
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