Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Leptospirosis in northern Tanzania: exploring the role of rodents and ruminant livestock in a neglected public health problem

Leptospirosis is an important but neglected zoonotic disease that is often overlooked in Africa. Although comprehensive data on the incidence of human disease are lacking, robust evidence of infection has been demonstrated in people and animals from all regions of the continent. However, to date, there are few examples of direct epidemiological linkages between human disease and animal infection. In East Africa, awareness of the importance of human leptospirosis as a cause of non-malarial febrile illness is growing. In northern Tanzania, acute leptospirosis has been diagnosed in 9% of patients with severe febrile illness compared to only 2% with malaria. However, little is known about the relative importance of different potential animal hosts as sources of human infection in this area. This project was established to investigate the roles of rodents and ruminant livestock, important hosts of Leptospira in other settings, in the epidemiology of leptospirosis in northern Tanzania. A cross-sectional survey of rodents living in and around human settlements was performed alongside an abattoir survey of ruminant livestock. Unusual patterns of animal infection were detected by real-time PCR detection. Renal Leptospira infection was absent from rodents but was detected in cattle from several geographic areas. Infection was demonstrated for the first time in small ruminants sub-Saharan Africa. Two major Leptospira species and a novel Leptospira genotype were detected in livestock. L. borgpetersenii was seen only in cattle but L. kirschneri infection was detected in multiple livestock species (cattle, sheep and goats), suggesting that at least two distinct patterns of Leptospira infection occur in livestock in northern Tanzania. Analysis of samples from acute leptospirosis in febrile human patients could not detect Leptospira DNA by real-time PCR but identified social and behavioural factors that may limit the utility of acute-phase diagnostic tests in this community. Analysis of serological data revealed considerable overlap between serogroups detected in cattle and human leptospirosis cases. Human disease was most commonly attributed to the serogroups Mini and Australis, which were also predominant reactive serogroups in cattle. Collectively, the results of this study led to the hypothesis that livestock are an important reservoir of Leptospira infection for people in northern Tanzania. These results also challenge our understanding of the relationship between Leptospira and common invasive rodent species, which do not appear to maintain infection in this setting. Livestock Leptospira infection has substantial potential to affect the well-being of people in East Africa, through direct transmission of infection or through indirect effects on food production and economic security. Further research is needed to quantify the impact of livestock leptospirosis in Africa and to develop effective interventions for the control of human and animal disease.

Investigating problem-based learning in Saudi Arabian mathematics education: a TIMSS-related study

The aim of this study is to investigate the effectiveness of problem-based learning (PBL) on students’ mathematical performance. This includes mathematics achievement and students’ attitudes towards mathematics for third and eighth grade students in Saudi Arabia. Mathematics achievement includes, knowing, applying, and reasoning domains, while students’ attitudes towards mathematics covers, ‘Like learning mathematics’, ‘value mathematics’, and ‘a confidence to learn mathematics’. This study goes deeper to examine the interaction of a PBL teaching strategy, with trained face-to-face and self-directed learning teachers, on students’ performance (mathematics achievement and attitudes towards mathematics). It also examines the interaction between different ability levels of students (high and low levels) with a PBL teaching strategy (with trained face-to-face or self-directed learning teachers) on students’ performance. It draws upon findings and techniques of the TIMSS international benchmarking studies. Mixed methods are used to analyse the quasi-experimental study data. One -way ANOVA, Mixed ANOVA, and paired t-tests models are used to analyse quantitative data, while a semi-structured interview with teachers, and author’s observations are used to enrich understanding of PBL and mathematical performance. The findings show that the PBL teaching strategy significantly improves students’ knowledge application, and is better than the traditional teaching methods among third grade students. This improvement, however, occurred only with the trained face-to-face teacher’s group. Furthermore, there is robust evidence that using a PBL teaching strategy could raise significantly students’ liking of learning mathematics, and confidence to learn mathematics, more than traditional teaching methods among third grade students. Howe ver, there was no evidence that PBL could improve students’ performance (mathematics achievement and attitudes towards mathematics), more than traditional teaching methods, among eighth grade students. In 8th grade, the findings for low achieving students show significant improvement compared to high achieving students, whether PBL is applied or not. However, for 3th grade students, no significant difference in mathematical achievement between high and low achieving students was found. The results were not expected for high achieving students and this is also discussed. The implications of these findings for mathematics education in Saudi Arabia are considered.