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This thesis is a result of the work of the many people at the TRIUMF laboratory who contributed in innumerable ways to providing the muons and constructing our experiments.

Thanks go to all the people who worked some very long days and nights to collect the data: Tanya Riseman, Kim Chow, Tim Duty, Masa Senba and Sarah Dunsiger, and the TRIUMF $\mu{\cal SR} $facility staff Mel Good, Curtis Ballard, Bassam Hitti, Don Arseneau and Syd Kreitzman for their support in both setting up and running these experiments.

I am very grateful to Slava Storchak, whose ideas and hard work took our experiments far, Dr. Nikolai V. Prokof'ev, for discussions and notes from which I learned quantum diffusion, and my committee members Drs. Walter Hardy, Rob Kiefl and Philip Stamp for their suggestions and encouragement. I would especially like to thank my thesis advisor Jess Brewer, whose idea it was to study cryocrystals, for guiding these experiments from their beginning, and for his suggestions, corrections and help in bringing this thesis to completion.