Nonequilibrium Statistical Models: Guided Network Growth Under Localized Information and Perspectives on Electron Diffusion in Conductors
Datum
2018-10-31
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University of Oregon
Zusammenfassung
The ability to probe many-particle systems on a microscopic level has revolutionized the
way we do statistical physics. As computational capabilities continue to grow exponentially, larger
and more complex systems come within reach of microscopic analysis. In the field of network
growth, the classical model has given way to competitive processes, in which networks are guided
by some criteria at every step of their formation. We develop and analyze a new competitive
growth process that permits intervention on growing networks using only local properties of the
network when evaluating how to add new connections. We establish the critical behavior of this
new method and explore potential uses in guiding the development of real-world networks.
The classical system of electrons diffusing within a conductor similarly permits a
microscopic analysis where, to date, studies of the macroscopic properties have dominated the
literature. In order to extend our understanding of the theory that governs this diffusion—the
fluctuation-dissipation theorem—we construct a physical model of the Johnson-Nyquist system
of electrons embedded in the bulk of a conductor. Constructing the model involves deriving how
the motion of each individual electron comes about via scattering processes in the conductor, then
connecting this collective motion to the macroscopic observables of voltage and current that define
Johnson-Nyquist noise. Once the equilibrium properties have been fully realized, an external
perturbation can be applied in order to probe the behavior of the model as it deviates away from
equilibrium. In much the same way that competitive network growth revolutionized classical
network theory, we aim to establish a model which can guide future research into nonequilibrium
fluctuation-dissipation by providing a method for interacting with the system in a precise and
well-controlled manner as it evolves over time. This model is presented in its present form in
Chapter 3.
Chapter 2, which covers this work, has been published in Physical Review E as a Rapid
Communication [1]. The writing and analysis were performed by me as the primary author. Eric
Corwin and Georgios Tsekenis are listed as co-authors for their contribution to the analysis and
for advisement on the work.
This dissertation includes previously published and unpublished co-authored material.
Beschreibung
Schlagwörter
Network theory, Statistical modeling