4,853 research outputs found
New Solvable Singular Potentials
We obtain three new solvable, real, shape invariant potentials starting from
the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on
the half-axis and extending their domain to the full line, while taking special
care to regularize the inverse square singularity at the origin. The
regularization procedure gives rise to a delta-function behavior at the origin.
Our new systems possess underlying non-linear potential algebras, which can
also be used to determine their spectra analytically.Comment: 19 pages, 4 figure
Quasiparticle interference in multiband superconductors with strong coupling
We develop a theory of the quasiparticle interference (QPI) in multiband
superconductors based on strong-coupling Eliashberg approach within the Born
approximation. In the framework of this theory, we study dependencies of the
QPI response function in the multiband superconductors with nodeless s-wave
superconductive order parameter. We pay a special attention to the difference
of the quasiparticle scattering between the bands having the same and opposite
signs of the order parameter. We show that, at the momentum values close to the
momentum transfer between two bands, the energy dependence of the quasiparticle
interference response function has three singularities. Two of these correspond
to the values of the gap functions and the third one depends on both the gaps
and the transfer momentum. We argue that only the singularity near the smallest
band gap may be used as an universal tool to distinguish between and
order parameters. The robustness of the sign of the response function
peak near the smaller gap value, irrespective of the change in parameters, in
both the symmetry cases is a promising feature that can be harnessed
experimentally.Comment: 16 pages, 16 figure
Coordinate Realizations of Deformed Lie Algebras with Three Generators
Differential realizations in coordinate space for deformed Lie algebras with
three generators are obtained using bosonic creation and annihilation operators
satisfying Heisenberg commutation relations. The unified treatment presented
here contains as special cases all previously given coordinate realizations of
and their deformations. Applications to physical problems
involving eigenvalue determination in nonrelativistic quantum mechanics are
discussed.Comment: 11 pages, 0 figure
Squeezing lepton pairs out of broken symmetries
We discuss two possible signatures of symmetry breaking that can appear in
dilepton spectra, as measured in relativistic heavy ion collisions. The first
involves scalar-vector meson mixing and is related to the breaking of Lorentz
symmetry by a hot medium. The second is related to the breaking of Furry's
theorem by a charged quark-gluon plasma. Those signals will be accessible to
upcoming measurements to be performed at the GSI, RHIC, and the LHC.Comment: 5 pages, 4 figures, talk given at the INPC 2001 (International
Conference on Nuclear Physics), 30 July - 3 August 2001, Berkeley, C
Meson Mixing and Dilepton Production in Heavy Ion Collisions
We study the possibility of mixing via N-N excitations in dense
nuclear matter. This mixing is found to induce a peak in the dilepton spectra
at an invariant mass equal to that of the . We calculate the cross section
for dilepton production through mixing and we compare its size with that of
annihilation. In-medium masses and mixing angles are also calculated.
Some preliminary results of the mixing effect on the dilepton production rates
at finite temperature are also presented.Comment: To be published in the proceedings of CIPANP 200
Analytical parametrization of fusion barriers using proximity potentials
Using the three versions of proximity potentials, namely proximity 1977,
proximity 1988, and proximity 2000, we present a pocket formula for fusion
barrier heights and positions. This was achieved by analyzing as many as 400
reactions with mass between 15 and 296. Our parametrized formula can reproduced
the exact barrier heights and positions within an accuracy of . A
comparison with the experimental data is also in good agreement.Comment: 12 pages, 5 figure
Algebraic Shape Invariant Models
Motivated by the shape invariance condition in supersymmetric quantum
mechanics, we develop an algebraic framework for shape invariant Hamiltonians
with a general change of parameters. This approach involves nonlinear
generalizations of Lie algebras. Our work extends previous results showing the
equivalence of shape invariant potentials involving translational change of
parameters with standard potential algebra for Natanzon type
potentials.Comment: 8 pages, 2 figure
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
Relativistic shape invariant potentials
Dirac equation for a charged spinor in electromagnetic field is written for
special cases of spherically symmetric potentials. This facilitates the
introduction of relativistic extensions of shape invariant potential classes.
We obtain the relativistic spectra and spinor wavefunctions for all potentials
in one of these classes. The nonrelativistic limit reproduces the usual
Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected
and replaced by two new statement
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