Quantum Free Particle Superoscillations in 1+1 Dimensions: A First-Quantised Approach

The principal differences between non-relativistic and relativistic quantum mechanics are: the existence of negative energy states, and the natural emergence of spin within a relativistic framework. We consider both these effects in the creation and evolution of superoscillating wavepackets. Superoscillations are a phenomena in which a function can oscillate faster than it’s fastest Fourier component. As a trade-off they suffer by being exponentially smaller than conventional oscillations. Previous studies of superoscillations within the construct of the Schrödinger equation have identified two key features: disappearance after a time, $t_d$, and an asymmetrical evolution either side of a line in space (the wall effect). In this thesis, we expand this work into a relativistic framework by applying it to the Klein-Gordon and Dirac equations, to do this we require a thorough examination of 1+1 dimensional relativistic propagators. Although initially derived interms of Bessel functions, these have two key limits which allow for simpler calculation: the light-cone limit $(x→x0+ct)$ and the WKB limit $(h→0)$. Positive and negative energy superoscillations are best described in the WKBlimit. Through application of asymptotic integration, we find that both positiveand negative energy superoscillations possess a disappearance time and wall effect. For both Klein Gordon and Dirac equations, $t_d$ is equal. This implies, in terms of disappearance spin has no effect on the evolution of a superoscillatory, relativistic wavefunction of positive or negative energy. However, relativistic superoscillations disappear faster than non-relativistic superoscillations, and in each case, the disappearance time tends to a finite value as a superoscillatory parameter is increased. For non-relativistic superoscillations $t_d→$1/2 compared to $t_d→$0.3715 for the relativistic case. The wall effect is also noticeably different in relativistic and non-relativistic contexts. The walls appear at different points in space and, despite the relativistic wall effect being evident from $t=$0, within the Schrödinger equation, it doesn’t appear until a time of $t=$1/32. This contrast in the wall effects of both cases is the leading cause of the inequality of the disappearance times. The asymmetries between the wall effects are caused by differences in the behaviour of saddles (complex momenta) found when evaluating the wavefunction as an integral over the propagator. Again, there is no disparity between the walls of the Klein-Gordon or Dirac equation; spin does not affect the evolution of positive ornegative energy superoscillations. Where positive and negative energy wavefunctions appear as $h→$0, mixed energy superoscillations appear at the light-cone. Mixed energy superoscillations do not exhibit the wall effect and neither do they exist in a non-relativistic description. However, they do have a disappearance time. In contrast to the positive and negative energy states,$t_d→$0 as a superoscillatory parameter is increased. It is within a mixed energy construct that the effect of spin on the evolution of relativistic superoscillations appears; one of the components of the Dirac equation does not superoscillate. This is caused by this term existing at the WKB limit as opposed to the light-cone

Evolution of superoscillations in a relativistic wavepacket

We analyse the evolution of superoscillations in a relativistic wavepacket. A simple superoscillat- ing wavepacket is set up and is allowed to evolve freely according to both the Klein-Gordon equation and the Dirac equation. The superoscillations evolve anisotropically and decay after a time. Both the lifetime and anisotropy can be understood in terms of the interaction of contributions to the wavepacket from components with strongly diering complex wavenumber. The analysis is sup- ported by numerical calculations and the results are compared with the non-relativistic analysis

Psychoeducation and Breathing Training for Stress Reduction in Student Athletes

Student athletes are exposed to many stressors across their university career and must juggle academic study and athletic pursuits. One simple and accessible relaxation technique is slow paced breathing (SPB). SPB is recognised as an effective stress management technique and can be used in high stress environments such as sport. Breathing at a specific pace (6 cycles per minute) triggers the resonance properties of the cardiovascular system and results in an increase in cardiac vagal activity (CVA), which may lead to reduced stress and enhanced wellbeing. Therefore, the aim of this study was to investigate the effectiveness of a psychoeducation and SPB intervention upon psychological stress, wellbeing and CVA in student athletes. Following institutional ethical approval, eight student athletes (Mage=20.75, SD=1.38, 3 female) competing at either national or international level were involved in the intervention. Athletes attended four sessions: 1. baseline screening 2. education workshop 3. post-intervention screening and 4. follow up focus group). In session one athletes completed measures of psychological distress (Physical Health Questionnaire-9, The Generalised Anxiety Disorder Assessment -7), overall wellbeing and knowledge of SPB. Athletes then completed a stress test involving stress induction using a script and a Stroop task, during which subjective stress and CVA was measured at rest, task and recovery. In session two athletes were educated about the benefits of SPB, trained to effectively use SPB, and practiced SPB in stressful conditions. After session two athletes practiced SPB daily for five minutes over a four-week period using a smart phone application, kept diaries of their progress and each week reported general wellbeing. After this period athletes returned for session three in which session one measures were repeated (one athlete did not complete these measures). Session four assessed the effectiveness of the intervention through a focus group. Preliminary analysis using paired samples t-tests found no significant differences in psychological distress pre (M=9.50, SD=8.03) to post (M=4.50, SD=4.03) intervention (t(6)=1.663, p=.14) and no change in overall wellbeing from pre (M=69.14, SD=16.98) to post (M=76.14, SD=13.65) intervention (t=-1.206(6), p=.27). Focus groups were thematically analysed, themes identified included using SPB for relaxation and sleep, SPB in performance, SPB use outside of sport. Athletes reported SPB increased bodily relaxation before going to sleep, nervousness reduced before games and helped to refocus during performance. The findings suggest SPB may be successfully delivered via smart phones if athletes are educated effectively and may influence subjective stress management, sleep and performance

Retrospective validation study of miniPIERS prediction model in Zanzibar

Objective: To perform a retrospective external validation of miniPIERS in Zanzibar's referral hospital. Methods: From February to December 2017, data were collected retrospectively on all cases of hypertensive disorders of pregnancy (HDP) admitted to Mnazi Mmoja Hospital, Zanzibar, Tanzania. The primary outcome was the predictive performance of miniPIERS by examining measures of discrimination, calibration, and stratification accuracy. The secondary outcome was the applicability of miniPIERS within the referral hospital setting. Results: During this period, 2218 of 13 395 (21%) patients were identified with HDP, of whom 594 met the inclusion criteria. Sixty per cent of patients with adverse outcomes were excluded because they had experienced one of the adverse outcomes before admission. The discriminative ability of miniPIERS was inaccurate. It was not likely to aid risk stratification because of low sensitivity and low positive predictive value. The model showed fair discrimination in HDP before 34 weeks of gestation (area under the receiver operating characteristics curve 0.72, 95% confidence interval 0.63–0.82). Conclusions: The benefit of miniPIERS appeared to be limited, although clinical conditions make any validation challenging. Its application for risk stratification in preterm pregnancies should be further investigated

"I lost my happiness, I felt half dead and half alive" - a qualitative study of the long-term aftermath of obstetric near-miss in the urban district of Zanzibar, Tanzania

Background: This study aims to explore the stories of three women from Zanzibar, Tanzania, who survived life-threatening obstetric complications. Their narratives will increase understanding of the individual and community-level burden masked behind the statistics of maternal morbidity and mortality in Tanzania. In line with

Mental health and quality of life of women one year after maternal near-miss in low and middle-income countries: The case of zanzibar, Tanzania

Women who experienced a maternal near-miss are at risk of mental health complications and lower quality of life, but long-term consequences are largely unknown. The aim of this study is to assess whether mental health symptoms and quality of life change over time and to examine associations with risk factors among post-partum women. In this cohort study, women with maternal near-miss were matched to women without or with mild complications at Mnazi Mmoja Hospital in Zanzibar. Depressive and post-traumatic stress disorder symptoms, and quality of life were measured at three, six, and twelve-months follow-up. A linear mixed-effects model was used for data analysis. Postpartum women in Zanzibar reported low levels of depressive and post-traumatic stress disorder symptoms. While depressive symptoms and quality of life trajectories were similar among women with and without maternal near-miss, differences for trajectories of post-traumatic stress disorder symptoms and physical quality of life were found. Social support, perinatal loss, and intercurrent illness were strongly associated with both depressive symptoms and quality of life in this group of Islamic women. These findings suggest that social support, embedded in the cultural context, should be considered in helping women cope with mental health issues in the aftermath of severe maternal complications

Journey to facility birth in Zanzibar: A questionnaire-based cohort study of patients' perspectives on preparedness, access and quality of care

Introduction Tackling substandard maternity care in health facilities requires engaging women's perspectives in strategies to improve outcomes. This study aims to provide insights in the perspectives of women with severe maternal morbidity on preparedness, access and quality of care in Zanzibar's referral hospital. Methods In a prospective cohort from April 2017 to December 2018, we performed semistructured interviews with women who experienced maternal near-miss complications and matched controls. These focused on sociodemographic and obstetric characteristics, perceived accessibility to and quality of facility care with 15 domains, scored on a one-to-five scale. Participants' comments and answers to open questions were employed to illustrate quantitative outcomes. Zanzibar's Medical Research and Ethics Committee approved the study (ZAMREC/0002/JUN/17). Results We included 174 cases and 151 controls. Compared with controls, patients with a near-miss had less formal education (p=0.049), perceived their wealth as poor (p=0.002) and had a stillbirth more often (p<0.001). Many experienced a delay in deciding to seek care. More than controls, near-miss patients experienced barriers in reaching care (p=0.049), often of financial nature (13.8% vs 4.0%). Quality of care was perceived as high, with means above 3 out of 5, in 14 out of 15 domains. One-fifth had an overall suboptimal experience, mostly regarding informed choice and supplies availability. Additional comments were expressed by a minority of participants. Conclusion Most patients promptly sought, accessed and received maternity care in Zanzibar's referral hospital. A minority experienced barriers, mostly financial, in reaching care and more so among patients with near-miss complications. Quality of facility care was generally highly rated. However, some reported insightful critical perceptions. This study highlights the impact of sociodemographic differences on health, the value of involving patients in decisions regarding maternity care and the need to ensure availability of medical supplies, all which will contribute to improved maternal well-being