2,031 research outputs found
A search on Dirac equation
The solutions, in terms of orthogonal polynomials, of Dirac equation with
analytically solvable potentials are investigated within a novel formalism by
transforming the relativistic equation into a Schrodinger like one. Earlier
results are discussed in a unified framework and certain solutions of a large
class of potentials are given.Comment: 9 page
Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices
We give a uniform interpretation of the classical continuous Chebyshev's and
Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie
algebra gl(N), where N is any complex number. One can similarly interpret
Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials
corresponding to Lie superlagebras.
We also describe the real forms of gl(N), quasi-finite modules over gl(N),
and conditions for unitarity of the quasi-finite modules. Analogs of tensors
over gl(N) are also introduced.Comment: 25 pages, LaTe
h analogue of Newton's binomial formula
In this letter, the --analogue of Newton's binomial formula is obtained in
the --deformed quantum plane which does not have any --analogue. For
, this is just the usual one as it should be. Furthermore, the binomial
coefficients reduce to for . \\ Some properties of the
--binomial coefficients are also given. \\ Finally, I hope that such results
will contribute to an introduction of the --analogue of the well--known
functions, --special functions and --deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75
A search on the Nikiforov-Uvarov formalism
An alternative treatment is proposed for the calculations carried out within
the frame of Nikiforov-Uvarov method, which removes a drawback in the original
theory and by pass some difficulties in solving the Schrodinger equation. The
present procedure is illustrated with the example of orthogonal polynomials.
The relativistic extension of the formalism is discussed.Comment: 10 page
Discrete Darboux transformation for discrete polynomials of hypergeometric type
Darboux Transformation, well known in second order differential operator
theory, is applied here to the difference equation satisfied by the discrete
hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)
Comment on Vortex Mass and Quantum Tunneling of Vortices
Vortex mass in Fermi superfluids and superconductors and its influence on
quantum tunneling of vortices are discussed. The vortex mass is essentially
enhanced due to the fermion zero modes in the core of the vortex: the bound
states of the Bogoliubov qiasiparticles localized in the core. These bound
states form the normal component which is nonzero even in the low temperature
limit. In the collisionless regime , the normal component
trapped by the vortex is unbound from the normal component in the bulk
superfluid/superconductors and adds to the inertial mass of the moving vortex.
In the d-wave superconductors, the vortex mass has an additional factor
due to the gap nodes.Comment: 10 pages, no figures, version accepted in JETP Letter
Trace identities and their semiclassical implications
The compatibility of the semiclassical quantization of area-preserving maps
with some exact identities which follow from the unitarity of the quantum
evolution operator is discussed. The quantum identities involve relations
between traces of powers of the evolution operator. For classically {\it
integrable} maps, the semiclassical approximation is shown to be compatible
with the trace identities. This is done by the identification of stationary
phase manifolds which give the main contributions to the result. The same
technique is not applicable for {\it chaotic} maps, and the compatibility of
the semiclassical theory in this case remains unsettled. The compatibility of
the semiclassical quantization with the trace identities demonstrates the
crucial importance of non-diagonal contributions.Comment: LaTeX - IOP styl
Magnetic vortex as a ground state for micron-scale antiferromagnetic samples
Here we consider micron-sized samples with any axisymmetric body shape and
made with a canted antiferromagnet, like hematite or iron borate. We find that
its ground state can be a magnetic vortex with a topologically non-trivial
distribution of the sublattice magnetization and planar coreless
vortex-like structure for the net magnetization . For
antiferromagnetic samples in the vortex state, in addition to low-frequency
modes, we find high-frequency modes with frequencies over the range of hundreds
of gigahertz, including a mode localized in a region of radius 30--40 nm
near the vortex core.Comment: 20 pages, 1 figur
Vortex motion in a finite-size easy-plane ferromagnet and application to a nanodot
We study the motion of a non-planar vortex in a circular easy-plane
ferromagnet, which imitates a magnetic nanodot. Analysis was done using
numerical simulations and a new collective variable theory which includes the
coupling of Goldstone-like mode with the vortex center. Without magnetic field
the vortex follows a spiral orbit which we calculate. When a rotating in-plane
magnetic field is included, the vortex tends to a stable limit cycle which
exists in a significant range of field amplitude B and frequency for a
given system size L. For a fixed , the radius R of the orbital motion
is proportional to L while the orbital frequency varies as 1/L and is
significantly smaller than . Since the limit cycle is caused by the
interplay between the magnetization and the vortex motion, the internal mode is
essential in the collective variable theory which then gives the correct
estimate and dependency for the orbit radius . Using this
simple theory we indicate how an ac magnetic field can be used to control
vortices observed in real magnetic nanodots.Comment: 15 pages (RevTeX), 14 figures (eps
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