This thesis examines the interpretations derived from the Kac Ring Model, and the adding of a modification to the original model via “kick backs,” which can be interpreted to represent time reversals in the individual Kac rings. The results of this modification are analyzed, and their implications explored. There are three main parts to this thesis. Part 1 is a literature review which explains the working principles of the original Kac ring and explores its numerous applications. Part 2 describes the software and the theoretical & computational methodology used to implement the model and gather data. Part 3 analyzes the data gathered and makes a conclusion about its implications. There is an appendix included which contains some figures from Part 3 in a larger size, as it wasn’t possible to make the figures bigger within the text due to formatting.
We implemented the well-known Ising model in one dimension as a computer program and simulated its behavior with four algorithms: (i) the seminal Metropolis algorithm; (ii) the microcanonical algorithm described by Creutz in 1983; (iii) a variation on Creutz’s time-reversible algorithm allowing for bonds between spins to change dynamically; and (iv) a combination of the latter two algorithms in a manner reflecting the different timescales on which these two processes occur (“freezing” the bonds in place for part of the simulation). All variations on Creutz’s algorithm were symmetrical in time, and thus reversible. The first three algorithms all favored low-energy states of the spin lattice and generated the Boltzmann energy distribution after reaching thermal equilibrium, as expected, while the last algorithm broke from the Boltzmann distribution while the bonds were “frozen.” The interpretation of this result as a net increase to the system’s total entropy is consistent with the second law of thermodynamics, which leads to the relationship between maximum entropy and the Boltzmann distribution.
(3He) as a comagnetometer, polarization analyzer, and detector.
Systematic influences on the nEDM measurement investigated in this thesis include (a) room temperature measurements on polarized 3He in a measurement cell made from the same materials as the nEDM experiment, (b) research and development of the Superconducting QUantum Interference Devices (SQUID) which will be used in the nEDM experiment, (c) design contributions for an experiment with nearly all the same conditions as will be present in the nEDM experiment, and (d) scintillation studies in superfluid helium II generated from alpha particles which are fundamentally similar to the nEDM scintillation process. The result of this work are steps toward achievement of a new upper limit for the nEDM experiment at the SNS facility.
We present the results of experimentation with a superconducting nanowire that can be operated in two detection modes: i) as a kinetic inductance detector (KID) or ii) as a single photon detector (SPD). When operated as a KID mode in linear mode, the detectors are AC-biased with tones at their resonant frequencies of 45.85 and 91.81MHz. When operated as an SPD in Geiger mode, the resonators are DC biased through cryogenic bias tees and each photon produces a sharp voltage step followed by a ringdown signal at the resonant frequency of the detector. We show that a high AC bias in KID mode is inferior for photon counting experiments compared to operation in a DC-biased SPD mode due to the small fraction of time spent near the critical current with an AC bias. We find a photon count rate of $\Gamma_{KID} = 150~$photons/s/mA in a critically biased KID mode and a photon count rate of $\Gamma_{SPD} = 10^6~$photons/s/mA in SPD mode.
This dissertation additionally presents simulations of a DC-biased, frequency-multiplexed readout of SNSPD devices in Advanced Design System (ADS), LTspice, and Sonnet. A multiplexing factor of 100 is achievable with a total count rate of $>5$MHz. This readout could enable a 10000-pixel array for astronomy or quantum communications. Finally, we present a prototype array design based on lumped element components. An early implementation of the array is presented with 16 pixels in the frequency range of 74.9 to 161MHz. We find good agreement between simulation and experimental data in both the time domain and the frequency domain and present modifications for future versions of the array.