2,485 research outputs found
On the possibility of applying the quasi-isothermal St\"ackel's model to our Galaxy
An earlier derived quasi-isothermal St\"ackel's model of mass distribution in
stellar systems and the corresponding formula for space density are applied to
our Galaxy. The model rotation curve is fitted to HI kinematical data. The
structural and scale parameters of the model are estimated and the
corresponding density contours for our Galaxy are presented.Comment: 7 pages, 3 figures. Accepted for publication in Baltic Astronomy (BA
AC Conductance in Dense Array of the GeSi Quantum Dots in Si
Complex AC-conductance, , in the systems with dense
GeSi quantum dot (QD) arrays in Si has been determined from
simultaneous measurements of attenuation, ,
and velocity, , of surface acoustic waves (SAW)
with frequencies = 30-300 MHz as functions of transverse magnetic field 18 T in the temperature range = 1-20 K. It has been shown that in the
sample with dopant (B) concentration 8.2 cm at
temperatures 4 K the AC conductivity is dominated by hopping between
states localized in different QDs. The observed power-law temperature
dependence, , and weak frequency dependence,
, of the AC conductivity are consistent with
predictions of the two-site model for AC hopping conductivity for the case of
1, where is the SAW angular frequency and
is the typical population relaxation time. At 7 K the AC
conductivity is due to thermal activation of the carriers (holes) to the
mobility edge. In intermediate temperature region 4 7 K, where AC
conductivity is due to a combination of hops between QDs and diffusion on the
mobility edge, one succeeded to separate both contributions. Temperature
dependence of hopping contribution to the conductivity above 4.5 K
saturates, evidencing crossover to the regime where 1. From
crossover condition, = 1, the typical value, , of
the relaxation time has been determined.Comment: revtex, 3 pages, 6 figure
Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
For non-zero values, we present an analytical solution of the radial
Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris
approximation within the framework of the Asymptotic Iteration Method. The
bound state energy eigenvalues and corresponding wave functions are obtained
for a number of diatomic molecules and the results are compared with the
findings of the super-symmetry, the hypervirial perturbation, the
Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N
expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of
Physics A: Mathematical and Genera
Mathematical Structure of Relativistic Coulomb Integrals
We show that the diagonal matrix elements where
are the standard Dirac matrix operators
and the angular brackets denote the quantum-mechanical average for the
relativistic Coulomb problem, may be considered as difference analogs of the
radial wave functions. Such structure provides an independent way of obtaining
closed forms of these matrix elements by elementary methods of the theory of
difference equations without explicit evaluation of the integrals. Three-term
recurrence relations for each of these expectation values are derived as a
by-product. Transformation formulas for the corresponding generalized
hypergeometric series are discussed.Comment: 13 pages, no figure
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
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
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