Classical and quantum mechanics with chaos

This thesis is concerned with the study, classically and quantum mechanically, of the square billiard with particular attention to chaos in both cases. Classically, we show that the rotating square billiard has two regular limits with a mixture of order and chaos between, depending on an energy parameter, E. This parameter ranges from -2w(^2) to oo, where w is the angular rotation, corresponding to the two integrable limits. The rotating square billiard has simple enough geometry to permit us to elucidate that the mechanism for chaos with rotation or curved trajectories is not flyaway, as previously suggested, but rather the accumulation of angular dispersion from a rotating line. Furthermore, we find periodic cycles which have asymmetric trajectories, below the value of E at which phase space becomes disjointed. These trajectories exhibit both left and right hand curvatures due to the fine balance between Centrifugal and Coriolis forces. Quantum mechanically, we compare the spectral analysis results for the square billiard with three different theoretical distribution functions. A new feature in the study is the correspondence we find, by utilising the Berry-Robnik parameter q, between classical E and a quantum rotation parameter w. The parameter q gives the ratio of chaotic quantum phase volume which we can link to the ratio of chaotic phase volume found classically for varying values of E. We find good correspondence, in particular, the different values of q as w is varied reflect the births and subsequent destructions of the different periodic cycles. We also study wave packet dynamics, necessitating the adaptation of a one dimensional unitary integration method to the two dimensional square billiard. In concluding we suggest how this work may be used, with the aid of the chaotic phase volumes calculated, in future directions for research work

Socioeconomic trends in differential mortality among middle-aged males in Norway 1960-1990

This study is based on data from three censuses (1960, 1979, and 1980) linked to the cause of death statistics kept during a 10-year follow-up period subsequent to each census. Linkages have been made for each individual male aged 30-64 years at the time of the census, based on their Norwegian national personal identification numbers. Socioeconomic status categories are specified according to the Norwegian classification of socioeconomic status. The 10-year post-census follow-up periods have each been divided into two five-year periods, and mortality has been calculated for both, based on the subjects’ socioeconomic status at the outset of the 10-year period. The study showed a decrease in mortality for all socioeconomic status categories. However, the decrease was far more pronounced among mean-level and higher-level salaried employees than among unskilled workers, farmers and fishermen. An even larger socioeconomic gap appeared between the fates of mortality due to cardiovascular disease. There are indications that the gaps may be health- related, since workers’ mortality rate increased from the first to the second five-year period following a census, while the same pattern was not found for salaried employees

Case-cohort Methods for Survival Data on Families from Routine Registers

In the Nordic countries, there exist several registers containing information on diseases and risk factors for millions of individuals. This information can be linked into families by use of personal identification numbers, and represent a great opportunity for studying diseases that show familial aggregation. Due to the size of the registers, it is difficult to analyze the data by using traditional methods for multivariate survival analysis, such as frailty or copula models. Since the size of the cohort is known, case-cohort methods based on pseudo-likelihoods are suitable for analyzing the data. We present methods for sampling control families both with and without replacement, and with or without stratification. The data are stratified according to family size and covariate values. Depending on the sampling method, results from simulations indicate that one only needs to sample 1%-5% of the control families in order to get good efficiency compared to a traditional cohort analysis. We also provide an application to survival data from the Medical Birth Registry of Norway