26 research outputs found
Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States
We consider the multi-channel inverse scattering problem in one-dimension in
the presence of thresholds and bound states for a potential of finite support.
Utilizing the Levin representation, we derive the general Marchenko integral
equation for N-coupled channels and show that, unlike to the case of the radial
inverse scattering problem, the information on the bound state energies and
asymptotic normalization constants can be inferred from the reflection
coefficient matrix alone. Thus, given this matrix, the Marchenko inverse
scattering procedure can provide us with a unique multi-channel potential. The
relationship to supersymmetric partner potentials as well as possible
applications are discussed. The integral equation has been implemented
numerically and applied to several schematic examples showing the
characteristic features of multi-channel systems. A possible application of the
formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure
Phase shift effective range expansion from supersymmetric quantum mechanics
Supersymmetric or Darboux transformations are used to construct local phase
equivalent deep and shallow potentials for partial waves. We
associate the value of the orbital angular momentum with the asymptotic form of
the potential at infinity which allows us to introduce adequate long-distance
transformations. The approach is shown to be effective in getting the correct
phase shift effective range expansion. Applications are considered for the
and partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical
Review
PT-supersymmetric partner of a short-range square well
In a box of size , a spatially antisymmetric square-well potential of a
purely imaginary strength and size is interpreted as an
initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of
which are all real for . The first partner potential is constructed
in closed form and discussed.Comment: 8 pages, no figure, presented at PHHQP3, Istanbul, June 20-22, 2005,
to be published in Czech. J. Phy
Determination of two-body potentials from n-body spectra
We show how the two-body potential may be uniquely determined from n-body
spectra where the hypercentral approximation is valid. We illustrate this by
considering an harmonic oscillator potential which has been altered by changing
the energy or normalisation constant of the ground state of the n-body system
and finding how this modifies the two-body potential. It is shown that with
increasing number of particles the spectrum must be known more precisely to
obtain the two-body potential to the same degree of accuracy.Comment: 13 pages of text (LATEX), 3 figures (not included, available from
authors), NIKHEF-93-P
Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems
For a quantum mechanical system with broken supersymmetry, we present a
simple method of determining the ground state when the corresponding energy
eigenvalue is sufficiently small. A concise formula is derived for the
approximate ground state energy in an associated, well-separated, asymmetric
double-well-type potential. Our discussion is also relevant for the analysis of
the fermion bound state in the kink-antikink scalar background.Comment: revised version, to be pubilshed in PR
Non-adiabatic corrections to elastic scattering of halo nuclei
We derive the formalism for the leading order corrections to the adiabatic
approximation to the scattering of composite projectiles. Assuming a two-body
projectile of core plus loosely-bound valence particle and a model (the core
recoil model) in which the interaction of the valence particle and the target
can be neglected, we derive the non-adiabatic correction terms both exactly,
using a partial wave analysis, and using the eikonal approximation. Along with
the expected energy dependence of the corrections, there is also a strong
dependence on the valence-to-core mass ratio and on the strength of the
imaginary potential for the core-target interaction, which relates to
absorption of the core in its scattering by the target. The strength and
diffuseness of the core-target potential also determine the size of the
corrections. The first order non-adiabatic corrections were found to be smaller
than qualitative estimates would expect. The large absorption associated with
the core-target interaction in such halo nuclei as Be11 kills off most of the
non-adiabatic corrections. We give an improved estimate for the range of
validity of the adiabatic approximation when the valence-target interaction is
neglected, which includes the effect of core absorption. Some consideration was
given to the validity of the eikonal approximation in our calculations.Comment: 14 pages with 10 figures, REVTeX4, AMS-LaTeX v2.13, submitted to
Phys. Rev.
(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
-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
A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background
A new manner for deriving the exact potentials is presented. By making use of
conformal mappings, the general expression of the effective potentials deduced
under su(1,1) algebra can be brought back to the general Natanzon
hypergeometric potentials
Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons
The quaternion Dirac equation in presence of generalized electromagnetic
field has been discussed in terms of two gauge potentials of dyons.
Accordingly, the supersymmetry has been established consistently and thereafter
the one, two and component Dirac Spinors of generalized quaternion Dirac
equation of dyons for various energy and spin values are obtained for different
cases in order to understand the duality invariance between the electric and
magnetic constituents of dyons.Comment: Key words: Supersymmetry, quaternion, Dirac equation, dyons PACS No.:
11.30.Pb, 14.80.Ly, 03.65.G
Temporal population variability in local forest communities has mixed effects on tree species richness across a latitudinal gradient
Among the local processes that determine species diversity in ecological communities, fluctuation‐dependent mechanisms that are mediated by temporal variability in the abundances of species populations have received significant attention. Higher temporal variability in the abundances of species populations can increase the strength of temporal niche partitioning but can also increase the risk of species extinctions, such that the net effect on species coexistence is not clear. We quantified this temporal population variability for tree species in 21 large forest plots and found much greater variability for higher latitude plots with fewer tree species. A fitted mechanistic model showed that among the forest plots, the net effect of temporal population variability on tree species coexistence was usually negative, but sometimes positive or negligible. Therefore, our results suggest that temporal variability in the abundances of species populations has no clear negative or positive contribution to the latitudinal gradient in tree species richness