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In this thesis, we study the low-energy effective theory for the antiferromagnetic quantum critical metal in two dimensions. The theory has been the subject of intense study for more than twenty years, due to the novel physics of non-Fermi liquid metals and its potential relevance to high-temperature superconductors and heavy-fermion compounds. In the first part of the thesis, we present the perturbative study of the theory in 3 minus epsilon space dimensions by extending the earlier one-loop analysis to higher-loop orders. We show that the expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs even in the small epsilon limit due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared fixed point, and the epsilon expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive quantum corrections beyond the linear order in epsilon in the limit that the ratio of velocities vanishes. In the second part of the thesis, we present a nonperturbative solution to the theory in two dimensions based on an ansatz that is inspired by the perturbative analysis. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by the ratio of velocities that dynamically flows to zero in the low-energy limit. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures. / Thesis / Doctor of Philosophy (PhD)

Opioid abuse and in particular fentanyl, a synthetic opioid, has been of concern in the last decade. Fentanyl is an illicit drug of concern to due to its prevalence and potency. Research to date has focused on supporting law enforcement by developing methods suitable for chemical profiling and identifying fentanyl from various matrices. However, methods geared towards analysis of fentanyl isomeric analogues are rare. Analysis of isomers is challenging due to similar mass spectral fragmentation patterns and exhibiting co-elution using common gas chromatographic columns. Developing methods to use in forensic labs utilizing already available equipment will advance current capabilities in the detection of fentanyl compounds. Thus, investigation into alternative stationary phases and development of special gas-liquid chromatographic (GLC) based methods for isomeric fentanyl analogues has been done. Several studies were done to investigate the use of ionic liquid chromatographic phases in analyzing fentanyl analogues. The first study focused on investigating the thermal stability of ionic liquids to identify those suitable to withstand the high oven temperatures that was needed to elute fentanyl analogues in gas chromatography. Total synchronous fluorescence spectroscopy and differential scanning calorimetry were demonstrated to be sensitive enough to detect the decomposition products of ionic liquids. In the second study, gas chromatographic analysis was done on fentanyl analogues using an ionic liquid stationary phase as well as two commonly used stationary phases for comparison purposes. The applicability of the developed methods was tested using standard fentanyl analogue samples as well as in-house synthesized samples on all three columns. In the third study, quantitative structure property relationship equations were developed to predict the retention time of fentanyl analogues on two of the gas chromatographic stationary phases used in the second study.

Thesis (doctoral)--Universiteit van Amsterdam, 1989. / Summary also in Dutch. Includes bibliographical references.

Thesis (M.F.A.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaves 64-65).

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