arXiv subjects

Maarten DeKieviet

Publications and source records attributed to Maarten DeKieviet.

9 recordsLinked to original sources

arXiv2025

Friedmann-Robertson-Walker spacetimes from the perspective of geometric algebra

The intention of our paper is to provide a pedagogical application of geometric algebra to a particularly well-investigated system: We formulate the geometric and dynamical properties of Friedmann-Robertson-Walker spacetimes within the language of geometric algebra and re-derive the Friedmann-equations as the central cosmological equations. Through the geometric algebra-variant of the Raychaudhuri equations, we comment on the evolution of spacetime volumes, before illustrating conformal flatness as a central property of Friedmann-cosmologies. An important aspect of spacetime symmetries are the associated conservation laws, for which we provide a geometric algebra formulation of the Lie-derivatives, of the Killing equation and of conserved quantities in Friedmann-Robertson-Walker spacetimes. Finally, we discuss the gravitational dynamics of scalar fields, with their particular relevance in cosmology, for cosmic inflation, and for dark energy.

gr-qc↗

arXiv2024

General Relativity: New insights from a Geometric Algebra approach

In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so, we show how GA offers insightful information on the physical meaning of the connection coefficients, the Riemann tensor, and other geometrical quantities.

gr-qc↗

arXiv2024

Differential Forms vs Geometric Algebra: The quest for the best geometric language

Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree of geometrical content. In recent years, Geometric Algebra appeared claiming to be a unifying language for physics and mathematics with a high level of geometrical content. Its strength is based on the unification of the inner and outer product into a single geometric operation, and its easy interpretation. Given their similarities, in this article we compare both formalisms side-by-side to narrow the gap between them in literature. We present a direct translation including differential identities, integration theorems and various algebraic identities. As an illustrative example, we present the case of classical electrodynamics in both formalism and finish with their description of GR.

gr-qc↗

arXiv2016

Geometric phases causing lifetime modifications of metastable states of hydrogen

Externally applied electromagnetic fields in general have an influence on the width of atomic spectral lines. The decay rates of atomic states can also be affected by the geometry of an applied field configuration giving rise to an imaginary geometric phase. A specific chiral electromagnetic field configuration is presented which geometrically modifies the lifetimes of metastable states of hydrogen. We propose to extract the relevant observables in a realistic longitudinal atomic beam spin-echo apparatus which allows the initial and final fluxes of the metastable atoms to be compared with each other interferometrically. A geometry-induced change in lifetimes at the 5%-level is found, an effect large enough to be observed in an available experiment.

physics.atom-ph↗

arXiv2014

Synthetic versus Dirac monopoles

In some recent experiments the distinction between synthetic magnetic monopoles and Dirac monopoles has been blurred. A case in point is the work in a letter by Ray {\it et al.} [arXiv:1408.3133] in which a beautiful experiment is reported but claims with regard to Dirac monopoles are misleading.

hep-th↗

arXiv2013

Quantum reflection from an oscillating surface

We describe an experimentally realistic situation of the quantum reflection of helium atoms from an oscillating surface. The temporal modulation of the potential induces clear sidebands in the reflection probability as a function of momentum. Theses sidebands could be exploited to slow down atoms and molecules in the experiment.

quant-ph↗

arXiv2013

Noble gas, alkali and alkaline atoms interacting with a gold surface

The attractive branch of the interaction potentials with the surface of gold have been computed for a large variety of atomic systems: the hydrogen atom, noble gases (He, Ne, Ar, Kr, Xe), alkali atoms (Li, Na, K, Rb, Cs) and alkaline atoms (Be, Mg, Ca, Sr, Ba). The results include highly accurate dynamic polarizabilities for the helium atom calculated using a variational method and explicitly correlated wavefunctions. For other atoms considered we used the data available in the literature. The interaction potentials include both the effects of retardation of the electromagnetic interactions and a realistic representation of the optical response function of gold (beyond the approximation of a perfect conductor). An explicit comparison of our result to the interaction between an atom and a perfect conductor is given.

physics.atom-ph↗

arXiv2009

Nonperturbative access to Casimir-Polder forces

We discuss the scalar analogue of the Casimir-Polder force between a sphere and a uniaxially corrugated surface with Dirichlet boundary conditions. Presenting a formulation that is nonperturbative in the height profile of the surface, we give explicit numerical results for a sinuosoidal corrugation profile.

quant-ph↗

arXiv2008

Scalar Casimir-Polder forces for uniaxial corrugations

We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces between an atom and a surface with arbitrary uniaxial corrugations. The complexity of the problem can be reduced to a one-dimensional Green's function equation along the corrugation which can be solved numerically. Our technique is fully nonperturbative in the height profile of the corrugation. We present explicit results for experimentally relevant sinusoidal and sawtooth corrugations. Parameterizing the deviations from the planar limit in terms of an anomalous dimension which measures the power-law deviation from the planar case, we observe up to order-one anomalous dimensions at small and intermediate scales and a universal regime at larger distances. This large-distance universality can be understood from the fact that the relevant fluctuations average over corrugation structures smaller than the atom-wall distance.

quant-ph↗