Physics Theses and Dissertations

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https://hdl.handle.net/1794/2048

This collection contains some of the theses and dissertations produced by students in the University of Oregon Physics Graduate Program. Paper copies of these and other dissertations and theses are available through the UO Libraries.

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Browsing Physics Theses and Dissertations by Subject "anomalous diffusion"

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    Lévy Motion and Cold Atoms
    (University of Oregon, 2020-09-24) Erickson, Wesley; Steck, Daniel
    Lévy processes are a universal model for characterizing the behavior of extreme events and anomalously diffusive systems. They are also important in modeling the transport of laser-cooled atoms. This dissertation contributes to the understanding of Lévy processes themselves, and to their application in laser-cooled atomic dynamics. Lévy processes are models of systems that contain extreme events. However, since any particular event could, upon closer inspection, be composed of multiple smaller events, what makes an event “extreme”? To answer this question it is useful to consider the history of the event, by studying Lévy processes conditioned to have a fixed final state at some later time. We find that events that greatly exceed a particular threshold are more likely to be composed of many small events and a single large event, rather than a series of comparably sized events. Analysis of the source of this threshold helps clarify the Gaussian limit of Lévy processes, and serves as the foundation for a useful distinction between “short” and “long” steps. These ideas also suggest possible experimental techniques that may be employed for cold atoms. Studies of anomalous diffusion in laser-cooled atoms have typically focused on the expansion profiles of clouds of cold atoms. However, the results of experiments and theoretical models have not been in close agreement, suggesting that existing models are still incomplete. To address this, it is important to develop alternative experimental approaches. One such approach is to use a single atom as a probe of the diffusion, which allows for the collection of boundary crossing statistics, such as the time between when an atom enters and leaves an imaging region. Through simulations, we find that distributions of these statistics develop peaks that correspond to atomic Lévy flights, in direct contrast to featureless power-law distributions for atoms undergoing Brownian motion. We find that characterizing these distributions gives information on the anomalous-diffusion exponent and typical velocities. Furthermore, these distributions serve as the basis for a method to directly detect Lévy flights at the level of a single atom.