143,143 research outputs found
Infinite Order Differential Operators in Spaces of Entire Functions
We study infinite order differential operators acting in the spaces of
exponential type entire functions. We derive conditions under which such
operators preserve the set of Laguerre entire functions which consists of the
polynomials possessing real nonpositive zeros only and of their uniform limits
on compact subsets of the complex plane. We obtain integral representations of
some particular cases of these operators and apply these results to obtain
explicit solutions to some Cauchy problems for diffusion equations with
nonconstant drift term
Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
Coquasitriangular universal matrices on quantum Lorentz and
quantum Poincar\'e groups are classified. The results extend (under certain
assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on
those objects are described.Comment: 18 pages, LaTeX file, minor change
The Dirac operator and gamma matrices for quantum Minkowski spaces
Gamma matrices for quantum Minkowski spaces are found. The invariance of the
corresponding Dirac operator is proven. We introduce momenta for spin 1/2
particles and get (in certain cases) formal solutions of the Dirac equation.Comment: 25 pages, LaTeX fil
The Deuteron Spin Structure Functions in the Bethe-Salpeter Approach and the Extraction of the Neutron Structure Function
The nuclear effects in the spin-dependent structure functions and
are calculated in the relativistic approach based on the Bethe-Salpeter
equation with a realistic meson-exchange potential.
The results of calculations are compared with the non-relativistic
calculations. The problem of extraction of the neutron spin structure function,
, from the deuteron data is discussed.Comment: (Talk given at the SPIN'94 International Symposium, September 15-22,
1994, Bloomington, Indiana), 6 pages, 5 figures, Preprint Alberta Thy 29-9
Critical velocity of superfluid flow through single barrier and periodic potentials
We investigate the problem of an ultracold atomic gas in the superfluid phase
flowing in the presence of a potential barrier or a periodic potential. We use
a hydrodynamic scheme in the local density approximation (LDA) to obtain an
analytic expression for the critical current as a function of the barrier
height or the lattice intensity, which applies to both Bose and Fermi
superfluids. In this scheme, the stationary flow becomes energetically unstable
when the local superfluid velocity is equal to the local sound velocity at the
point where the external potential is maximum. We compare this prediction with
the results of the numerical solutions of the Gross-Pitaevskii and
Bogoliubov-de Gennes equations. We discuss the role of long wavelength
excitations in determining the critical velocity. Our results allow one to
identify the different regimes of superfluid flow, namely, the LDA hydrodynamic
regime, the regime of quantum effects beyond LDA for weak barriers and the
regime of tunneling between weakly coupled superfluids for strong barriers. We
finally discuss the relevance of these results in the context of current
experiments with ultracold gases.Comment: 10 pages, 6 figures; appendix extended, to appear in Phys. Rev.
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