UC Berkeley

In this dissertation, I analyze certain problems in the following areas: 1) quantum dynamical phenomena in macroscopic systems of interacting, degenerate bosons (Parts II, III, and V), and 2) measures of macroscopicity for a large class of two-branch superposition states in separable Hilbert space (Part IV). Part I serves as an introduction to important concepts recurring in the later Parts. In Part II, a microscopic derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3 + 1)D microscopic model with local U(1) gauge symmetry is presented. The effective theory is applied to the transition from linear to sinusoidal current vs. phase behavior observed in recent experiments on liquid 4He driven through nanoaperture arrays. Part III discusses path-integral Monte Carlo (PIMC) numerical simulations of quantum hydrodynamic properties of reservoirs of He II communicating through simple nanoaperture arrays. In addition to calculating the local superfluid density in these systems, new estimators for hydrodynamic observables and novel methods for extracting the length scale characterizing the decay of superfluidity at the system boundary from PIMC data are introduced with the aim of exploring the mechanism of superfluid weak-link formation in nanoscale containers.

Part IV consists of an analysis of macroscopicity measures for a large class of Schrodinger cat states of N-mode photonic systems. For cat states of this class, it is shown that a well-known measure of superposition size based on the optimal distinguishability of the branches and another based on metrological usefulness of the superposition relative to its branches agree (i.e., designate the same superpositions as macroscopic) when the inner product of the branches of the superposition is sufficiently small. For certain superpositions in this class, a technique is presented for deriving a state-specific textit{metrological macroscopicity algebra} of observables. The dynamics of superposition size measures is also considered, leading to the notion of "distinguishability time,'' a generalization of the orthogonalization times of Mandelstam-Tamm and Margolus-Levitin.

In Part V, an investigation of the nonequilibrium dynamics of a quantum dot-Josephson junction-quantum dot nanodevice is presented. The nonequilibrium action of the system is calculated by making use of the Keldysh formalism and a potential use of the device for transferring macroscopic superposition states between a spin-system and an s-wave superconductor is discussed.