Reflection of matter waves in potential structures

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.

Adiabatic propagation in potential structures

In this work the adiabatic approximation is applied to the propagation of matter waves in confined geometries like those experimentally realized in recent atom optical experiments. Adiabatic propagation along a channel is assumed not to mix the various transverse modes. Nonadiabatic corrections arise from the potential squeezing and bending. Here we investigate the effect of the former. Detailed calculations of two-dimensional propagation are carried out both exactly and in an adiabatic approximation. This offers the possibility to analyze the validity of adiabaticity criteria. A semiclassical (sc) approach, based on the sc Massey parameter is shown to be inadequate, and the diffraction due to wave effects must be included separately. This brings in the Fresnel parameter well known from optical systems. Using these two parameters, we have an adequate understanding of adiabaticity on the system analyzed. Thus quantum adiabaticity must also take cognizance of the intrinsic diffraction of matter waves.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

Epistemic Modality in Linguistic and Literature Essays in English : A comparative corpus-based study of modal verbs in student claims

This study is a corpus-based comparison between student essays written in the subject areas of English linguistics and literature at undergraduate level. They are 200 Bachelor degree theses submitted at a variety of university departments (such as English, Language and Literature, Humanities, Social and Intercultural Studies) in Sweden. The comparison concerns frequencies of core modal verbs and how often they occur together with the I, we and it subject pronouns and in the structures this/the [essay, study, project, thesis] when students attempt to communicate their personal claims. Quantitative and qualitative analyses of the essays show few similarities in the ways that core modal verbs appear in both disciplines. The results indicate mainly distinct differences, especially in relation to clusters and variation of performative verbs. Specific patterns in the ways that students use core modal verbs as hedges have also been identified.