Date of Award

Spring 5-2025

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics, Applied

First Advisor

Maxim Olshanii

Second Advisor

Olga Goulko

Third Advisor

Stephen Arnason

Abstract

This dissertation addresses three main themes: cold atoms, integrability, and number theory. In this dissertation we present novel approaches to four models, each of which touches on at least two of the three themes. At the intersection of cold atoms and integrability, we present a Lagrange bracket formalism that allows for exact computation of initial quantum fluctuations of soliton breathers which previously could only be estimated numerically, and the advance in software tools developed in Python to facilitate studies of two-dimensional disc breathers. At the intersection of integrability and number theory, we present a propagator for the Newman-Moore, or triangular plaquette, model for glassy spin systems derived from the Rule 60 cellular automaton which allows all ground states to be found for square lattices with side length equal to a Mersenne number. Finally, at the intersection of cold atoms, integrability, and number theory, we present a lattice WKB approximation and general solutions for a tight-binding lattice model with exponential hopping which arises from studies of a single atom in a specifically engineered potential.

Comments

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