2,676 research outputs found
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
Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu
We investigate the spectral theory of the invariant Landau Hamiltonian
\La^\nu acting on the space of
-automotphic functions on \C^n, for given real number ,
lattice of \C^n and a map such that the
triplet satisfies a Riemann-Dirac quantization type
condition. More precisely, we show that the eigenspace
{\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in
{\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f};
\lambda\in\C, is non trivial if and only if . In such
case, is a finite dimensional vector space
whose the dimension is given explicitly. We show also that the eigenspace
associated to the lowest Landau level of
\La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n),
of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma)
e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can
realize also as the null space of the differential operator
acting on
functions on \C^n satisfying .Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of
"Journal of Mathematical Physics
Motion of vortices in ferromagnetic spin-1 BEC
The paper investigates dynamics of nonsingular vortices in a ferromagnetic
spin-1 BEC, where spin and mass superfluidity coexist in the presence of
uniaxial anisotropy (linear and quadratic Zeeman effect). The analysis is based
on hydrodynamics following from the Gross-Pitaevskii theory. Cores of
nonsingular vortices are skyrmions with charge, which is tuned by uniaxial
anisotropy and can have any fractal value between 0 and 1. There are
circulations of mass and spin currents around these vortices. The results are
compared with the equation of vortex motion derived earlier in the
Landau-Lifshitz-Gilbert theory for magnetic vortices in easy-plane
ferromagnetic insulators. In the both cases the transverse gyrotropic force
(analog of the Magnus force in superfluid and classical hydrodynamics) is
proportional to the charge of skyrmions in vortex cores.Comment: 19 pages, 2 figures, to be published in the special issue of Fizika
Nizkikh Temperatur dedicated to A.M.Kosevich. arXiv admin note: substantial
text overlap with arXiv:1801.0109
Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential
The bound state energy eigenvalues and the corresponding eigenfunctions of
the generalized Woods Saxon potential are obtained in terms of the Jacobi
polynomials. Nikiforov Uvarov method is used in the calculations. It is shown
that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review
Crystal structure of mixed fluorites Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) and luminescence of Eu(2+) in the crystals
Within the framework of the virtual crystal method implemented in the shell
model and pair potential approximation the crystal structure of mixed fluorites
Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) has been calculated. The impurity center
Eu(2+) and the distance Eu(2+)-F in this crystals have been also calculated.
The low level position of excited 4f65d configuration of the Eu(2+) ion has
been expressed using phenomenological dependence on distance E(2+)-F. The
dependences of Stokes shift and Huang-Rhys factor on concentration x have been
received for yellow luminescence in Sr(1-x)Ba(x)F(2):Eu(2+). The value x, for
which the eg -level of Eu(2+) ion will be in conduction band in
Sr(1-x)Ba(x)F(2):Eu(2+) has been calculated.Comment: 8 pages, 3 figures. The manuscript is sent to journal 'Physics of the
solid state'. The results will be submitted on inernational conference
SCINTMAT'2002 in oral session (june,20-22,2002,Ekaterinburg,Russia).
Corresponding author e-mail: [email protected]
The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states
This is the first in a series of articles in which we study the rotating
Morse potential model for diatomic molecules in the tridiagonal J-matrix
representation. Here, we compute the bound states energy spectrum by
diagonalizing the finite dimensional Hamiltonian matrix of H2, LiH, HCl and CO
molecules for arbitrary angular momentum. The calculation was performed using
the J-matrix basis that supports a tridiagonal matrix representation for the
reference Hamiltonian. Our results for these diatomic molecules have been
compared with available numerical data satisfactorily. The proposed method is
handy, very efficient, and it enhances accuracy by combining analytic power
with a convergent and stable numerical technique.Comment: 18 Pages, 6 Tables, 4 Figure
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
Dephasing due to electron-electron interaction in a diffusive ring
We study the effect of the electron-electron interaction on the weak
localization correction of a ring pierced by a magnetic flux. We compute
exactly the path integral giving the magnetoconductivity for an isolated ring.
The results are interpreted in a time representation. This allows to
characterize the nature of the phase coherence relaxation in the ring. The
nature of the relaxation depends on the time regime (diffusive or ergodic) but
also on the harmonics of the magnetoconductivity. Whereas phase coherence
relaxation is non exponential for the harmonic , it is always exponential
for harmonics . Then we consider the case of a ring connected to
reservoirs and discuss the effect of connecting wires. We recover the behaviour
of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter
(compared to the Nyquist length). We also predict a new behaviour when the
Nyquist length exceeds the perimeter.Comment: 21 pages, RevTeX4, 8 eps figures; version of 10/2006 : eqs.(100-102)
of section V.C correcte
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