1,464 research outputs found
Scattering in the PT-symmetric Coulomb potential
Scattering on the -symmetric Coulomb potential is studied along a
U-shaped trajectory circumventing the origin in the complex plane from
below. This trajectory reflects 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 -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
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 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
Underlying events in p+p collisions at LHC energies
General properties of hadron production are investigated in proton-proton
collisions at LHC energies. We are interested in the characteristics of hadron
production outside the identified jet cones. We improve earlier definitions and
introduce surrounding rings/belts around the cone of identified jets. In this
way even multiple jet events can be studied in details. We define the
underlying event as collected hadrons from outside jet cones and outside
surrounding belts, and investigate the features of these hadrons. We use a
PYTHIA generated data sample of proton-proton collisions at s = (7 TeV)^2. This
data sample is analysed by our new method and the widely applied CDF method.
Angular correlations and momentum distributions have been studied and the
obtained results are compared and discussed.Comment: 5 pages, 5 figures, to appear in the EPJ Web of Conferences,
Proceedings of the International Workshop on Hot and Cold Baryonic Matter
2010 (Budapest, Hungary, 15-20 August 2010
The Nuclear Modification Factor at Large Rapidities
RHIC data on high- 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
collisions at energies GeV and 63 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
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.
Underlying Event Studies for LHC Energies
Underlying event was originally defined by the CDF collaboration decades ago.
Here we improve the original definition to extend our analysis for events with
multiple-jets. We introduce a definition for surrounding rings/belts and based
on this definition the jet- and surrounding-belt-excluded areas will provide a
good underlying event definition. We inverstigate our definition via the
multiplicity in the defined geometry. In parallel, mean transverse momenta of
these areas also studied in proton-proton collisions at TeV LHC
energy.Comment: 6 pages and 4 figure
Representation reduction and solution space contraction in quasi-exactly solvable systems
In quasi-exactly solvable problems partial analytic solution (energy spectrum
and associated wavefunctions) are obtained if some potential parameters are
assigned specific values. We introduce a new class in which exact solutions are
obtained at a given energy for a special set of values of the potential
parameters. To obtain a larger solution space one varies the energy over a
discrete set (the spectrum). A unified treatment that includes the standard as
well as the new class of quasi-exactly solvable problems is presented and few
examples (some of which are new) are given. The solution space is spanned by
discrete square integrable basis functions in which the matrix representation
of the Hamiltonian is tridiagonal. Imposing quasi-exact solvability constraints
result in a complete reduction of the representation into the direct sum of a
finite and infinite component. The finite is real and exactly solvable, whereas
the infinite is complex and associated with zero norm states. Consequently, the
whole physical space contracts to a finite dimensional subspace with
normalizable states.Comment: 25 pages, 4 figures (2 in color
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