Search results for "Vector operator"
showing 8 items of 8 documents
The Ramsey method in high-precision mass spectrometry with Penning traps: Theoretical foundations
2007
Abstract This paper presents in a quantum mechanical framework a theoretical description of the interconversion of the magnetron and modified cyclotron motional modes of ions in a Penning trap due to excitation by external rf-quadrupole fields with a frequency near the true cyclotron frequency. The work aims at a correct description of the resonance line shapes that are observed in connection with more complicated excitation schemes using several excitation pulses, such as Ramsey’s method of separated oscillating fields. Quantum mechanical arguments together with the “rotating wave approximation” suggest a model Hamiltonian that permits a rigorous solution of the corresponding Heisenberg eq…
A method of desingularization for analytic two-dimensional vector field families
1991
It is well known that isolated singularities of two dimensional analytic vector fields can be desingularized: after a finite number of blowing up operations we obtain a vector field that exhibits only elementary singularities. In the present paper we introduce a similar method to simplify the periodic limit sets of analytic families of vector fields. Although the method is applied here only to reduce to families in which the zero set has codimension at least two, we conjecture that it can be used in general. This is related to the famouss Hibert's problem about planar vector fields.
Off-forward Matrix Elements in Light-front Hamiltonian QCD
2002
We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.
The exterior derivative as a Killing vector field
1996
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.
Octupolar excitation of ion motion in a Penning trap: A theoretical study
2014
Abstract High-precision Penning-trap mass spectrometry uses the resonant conversion of the magnetron motional mode into the cyclotron motional mode to determine the cyclotron frequency of the ions under investigation. Usually the conversion process is performed by interaction of the ions with external quadrupolar rf-fields. Recently it was found that conversion by means of octupolar rf-fields entails a tremendous increase in mass resolution and is thus of great interest. However, the conversion results depend in an intricate way on the amplitudes and phases of the octupolar rf-field and of the motional modes of the ions. Experimental progress was hampered by the lack of an underlying theory…
Finite element approximation of vector fields given by curl and divergence
1981
In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.
General duality in vector optimization
1993
Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x 0 ∊ A w,0 ∊ Fx$0 such that w,0 is minimal in FA. To a family of vector minimization problemsminimize , one associates a Lagrange relation where ξ belongs to an arbitrary class Ξ of mappings, the main purpose being to recover solutions of the original problem from the vector minimization of the Lagrange relation for an appropriate ξ. This ξ turns out to be a solution of a dual vector maximization problem. Characterizations of exact and approximate duality in terms of vector (generalized with respect to Ξ) convexity and subdifferentiability are given. They extend the theory existin…
Minimal unit vector fields
2002
We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.