3,751 research outputs found
Algebraic treatment of the confluent Natanzon potentials
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas,
the Green's function for the class of the confluent Natanzon potentials is
constructed straightforwardly. The bound-state energy spectrum is then
determined. Eventually, the three-dimensional harmonic potential, the
three-dimensional Coulomb potential and the Morse potential may all be
considered as particular cases.Comment: 9 page
Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
We determine, for all three-dimensional non-unimodular Lie groups equipped
with a Lorentzian metric, the set of homogeneous geodesics through a point.
Together with the results of [C] and [CM2], this leads to the full
classification of three-dimensional Lorentzian g.o. spaces and naturally
reductive spaces
Pseudo-K\"ahler Lie algebras with abelian complex structures
We study Lie algebras endowed with an abelian complex structure which admit a
symplectic form compatible with the complex structure. We prove that each of
those Lie algebras is completely determined by a pair (U,H) where U is a
complex commutative associative algebra and H is a sesquilinear hermitian form
on U which verifies certain compatibility conditions with respect to the
associative product on U. The Riemannian and Ricci curvatures of the associated
pseudo-K\"ahler metric are studied and a characterization of those Lie algebras
which are Einstein but not Ricci flat is given. It is seen that all
pseudo-K\"ahler Lie algebras can be inductively described by a certain method
of double extensions applied to the associated complex asssociative commutative
algebras
Associated Production of a W Boson and One b Jet
We calculate the production of a W boson and a single b jet to
next-to-leading order in QCD at the Fermilab Tevatron and the CERN Large Hadron
Collider. Both exclusive and inclusive cross sections are presented. We
separately consider the cross section for jets containing a single b quark and
jets containing a b-anti b pair. There are a wide variety of processes that
contribute, and it is necessary to include them all in order to have a complete
description at both colliders.Comment: LaTeX, 16 pages, 22 postscript figures; version published in Phys.
Rev.
On the local existence of maximal slicings in spherically symmetric spacetimes
In this talk we show that any spherically symmetric spacetime admits locally
a maximal spacelike slicing. The above condition is reduced to solve a
decoupled system of first order quasi-linear partial differential equations.
The solution may be accomplished analytical or numerically. We provide a
general procedure to construct such maximal slicings.Comment: 4 pages. Accepted for publication in Journal of Physics: Conference
Series, Proceedings of the Spanish Relativity Meeting ERE200
Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD
The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative extra loop in order to recover the primitive (physical) variables, the analytical inversion of the implicit operator is trivial and the several stages can actually be viewed as stages of explicit Runge-Kutta methods with an effective time-step. We test these methods with two different one-dimensional test beds in varied conductivity regimes, and show that our second-order schemes satisfy the theoretical expectations
Dynamics of entropy and nonclassical properties of the state of a -type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium
In this paper, we study the interaction between a three-level atom and a
quantized single-mode field with intensity-dependent coupling in a Kerr medium.
The three-level atom is considered to be in a -type configuration.
Under particular initial conditions, which may be prepared for the atom and
the field, the dynamical state vector of the entire system will be explicitly
obtained, for arbitrary nonlinearity function associated to any physical
system.
Then, after evaluating the variation of the field entropy against time, we
will investigate the quantum statistics as well as some of the nonclassical
properties of the introduced state. During our calculations we investigate the
effects of intensity-dependent coupling, Kerr medium and detuning parameters on
the depth and domain of the nonclassicality features of the atom-field state
vector. Finally, we compare our obtained results with those of -type
three-level atoms.Comment: 18 pages, 7 Figure
The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions
We study certain families of oscillatory integrals ,
parametrised by phase functions and amplitude functions globally
defined on , which give rise to tempered distributions, avoiding
the standard homogeneity requirement on the phase function. The singularities
of are described both from the point of view of the lack of
smoothness as well as with respect to the decay at infinity. In particular, the
latter will depend on a version of the set of stationary points of ,
including elements lying at the boundary of the radial compactification of
. As applications, we consider some properties of the two-point
function of a free, massive, scalar relativistic field and of classes of global
Fourier integral operators on , with the latter defined in terms
of kernels of the form .Comment: 30 pages, 2 figures, mistakes and typos correctio
Local well-posedness for the nonlinear Schr\"odinger equation in the intersection of modulation spaces
We introduce a Littlewood-Paley characterization of modulation spaces and use
it to give an alternative proof of the algebra property, somehow implicitly
contained in Sugimoto (2011), of the intersection for , and
. We employ this algebra property to show the local well-posedness of
the Cauchy problem for the cubic nonlinear Schr\"odinger equation in the above
intersection. This improves Theorem 1.1 by B\'enyi and Okoudjou (2009), where
only the case is considered, and closes a gap in the literature. If and or if and then
and the
above intersection is superfluous. For this case we also reobtain a
H\"older-type inequality for modulation spaces.Comment: 14 page
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