Search results for "Vector"

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…

Analysis of Inhomogeneously Dielectric Filled Cavities Coupled to Dielectric-Loaded Waveguides: Application to the Study of NRD-Guide Components

2004

In this paper, we present two contributions. First, we develop a computationally efficient technique for the full-wave characterization of inhomogeneously dielectric-filled cavities connected to inhomogeneously dielectric-loaded waveguides. This method is based on the expansion of the electromagnetic field within the cavity in terms of their solenoidal and irrotational modes. The presented formulation allows the treatment of hybrid modes in the waveguide ports, where the definition of a characteristic modal impedance or admittance is not possible. The multimode scattering matrix of the structure is computed throughout an efficient implementation of the orthonormal-basis method for the calcu…

Interpretation of KPFM Data with the Weight Function for Charges

2018

The KPFM signal for systems containing local charges can be expressed as a weighted sum over all local charges. The weight function for charges quantifies the contribution of each charge, depending on its position. In this chapter, we evaluate the KPFM weight function for charges by analyzing several application-relevant model systems. The intention of this chapter is to provide insights into the KPFM contrast formation in order to facilitate the KPFM data interpretation. For this, we concentrate on three model systems: (A) a conductive sample in ultra-high vacuum, (B) a dielectric sample in ultra-high vacuum, and (C) a dielectric sample in water. We calculate the weight function for charge…

Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

2003

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

Covariant determination of the Weyl tensor geometry

2001

We give a covariant and deductive algorithm to determine, for every Petrov type, the geometric elements associated with the Weyl tensor: principal and other characteristic 2-forms, Debever null directions and canonical frames. We show the usefulness of these results by applying them in giving the explicit characterization of two families of metrics: static type I spacetimes and type III metrics with a hypersurface-orthogonal Killing vector. PACS numbers: 0240M, 0420C

Non-Linear Relativistic Evolution of Cosmological Perturbations in Irrotational Dust

2008

Dynamics of a Quantum Particle in Asymmetric Bistable Potential with Environmental Noise

2011

In this work we analyze the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir. We obtain the time evolution of the population distributions in both energy and position eigenstates of the particle, for different values of the coupling strength with the thermal bath. The calculation is carried out using the Feynman-Vernon functional under the discrete variable representation.

Driven harmonic oscillators in the adiabatic Magnus approximation

1993

The time evolution of driven harmonic oscillators is determined by applying the Magnus expansion in the basis set of instantaneous eigenstates of the total Hamiltonian. It is shown that the first-order approximation already provides transition probabilities close to the exact values even in the intermediate regime.

Transition cancellations of 87Rb and 85Rb atoms in a magnetic field

2020

We have analyzed the magnetic field dependencies of the intensities of all the optical transitions between magnetic sublevels of hyperfine levels, excited with σ + , π , and σ − polarized light, for the D 1 and D 2 lines of 87 R b and 85 R b atoms. Depending on the type of transition and the quantum numbers of the involved levels, the Hamiltonian matrices are of 1 × 1 , 2 × 2 , 3 × 3 , or 4 × 4 dimension. As an example, analytical expressions are presented for the case of 2 × 2 dimension matrices for the D 1 line of both isotopes. Eigenvalues and eigenkets are given, and the expression for the transition intensity as a function of B has been determined. It is found that some π transitions o…

Statistical description of soliton clustering in fiber lasers with slow-gain dynamics

2014

We demonstrate theoretically that the dynamic clustering of solitons observed in a variety of experiments are due to the initial phase and position of interacting solitons with the slow gain dynamics of the fiber laser.