The Path of Possibilities

by Ilan Averbuch presented to Brock in 1988.

Mackenzie Chown Path

Path running next to the Mackenzie Chown Complex.

Mackenzie Chown Path

View of the Complex and the path running along it from the east.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration /

Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate the exact expectation values, ($o|^|^o), of multiplicative operators, such as polarizabilities and high-order hyperpolarizabilities, for isolated atoms and molecules. The existing forward-walking pure diffusion Monte Carlo (FW-PDMC) algorithm which attempts this has a serious bias. On the other hand, the DMC algorithm with minimal stochastic reconfiguration provides unbiased estimates of the energies, but the expectation values ($o|^|^) are contaminated by ^, an user specified, approximate wave function, when A does not commute with the Hamiltonian. We modified the latter algorithm to obtain the exact expectation values for these operators, while at the same time eliminating the bias. To compare the efficiency of FW-PDMC and the modified DMC algorithms we calculated simple properties of the H atom, such as various functions of coordinates and polarizabilities. Using three non-exact wave functions, one of moderate quality and the others very crude, in each case the results are within statistical error of the exact values.

Minimal Contact Intervention for Tobacco Dependence

This study was conducted to measure the degree of adherence by public health care providers to a policy that requires them to implement minimal contact intervention for tobacco cessation with their clients. This study also described what components of the intervention may have contributed to the adherence of the policy and how health care providers felt about adhering to the policy. The intervention consisted of a policy for implementation of minimal contact intervention, changes to documentation, a health care provider mentor trained, a training session for health care providers, and ongoing paper and people supports for implementation. Data for this study were collected through a health care provider questionnaire, focus group interviews, and a compliance protocol including a chart audit. The findings of this study showed a high degree of adherence to the policy, that health care providers thought minimal contact intervention was important to conduct with their clients, and that health care providers felt supported to implement the intervention. No statistically significant difference was found between new and experienced health care providers on 17 of the 18 questions on the health care provider questionnaire. However there was a statistically significant difference between new and experienced health care providers with respect to their perception that “clients often feel like they have to accept tobacco cessation information from me.” Changes could be made to the minimal contact intervention and to documentation of the intervention. Implications for future research include implementation within other programs within Hamilton Public Health Services and implementation of this model within other public health units and other types of health care providers within Ontario.