Applications of Semiclassical Theory in Statistical and Quantum Mechanics
2018-06
Loading...
View/Download File
Persistent link to this item
Statistics
View StatisticsJournal Title
Journal ISSN
Volume Title
Title
Applications of Semiclassical Theory in Statistical and Quantum Mechanics
Authors
Published Date
2018-06
Publisher
Type
Thesis or Dissertation
Abstract
Since the initiation of quantum theory in the early 20th century, semiclassical methods have been a perenniel source of insight into a diverse range of phenomena. In spite of this history, however, there remain interesting and insightful applications of semiclassical theory to physics. This thesis advances this programme in several directions. First, we consider the statistical mechanics of multivalent 1D Coulomb gases and demonstrate how the semiclassical WKB method may be used to expose its thermodynamic properties. In doing so, we develop ideas from algebraic topology and complex Riemann surfaces. Moving to quantum theory proper, these tools are applied fruitfully to the phenomenon of spin tunneling oscillations in magnetic molecules with large instrinsic spin. Moving away from the WKB approximation, these ideas from complex analysis also proved crucial in exposing universal finite-size scaling effects in 1D lattice systems such as the Su-Schrieffer-Heeger model of polyacetylene and the Kitaev chain. Finally, we end by considering the the weak noise theory of the KPZ equation and thereby discover a novel phase transition in its large deviation statistics.
Description
University of Minnesota Ph.D. dissertation. June 2018. Major: Physics. Advisor: Alex Kamenev. 1 computer file (PDF); v, 96 pages.
Related to
Replaces
License
Collections
Series/Report Number
Funding information
Isbn identifier
Doi identifier
Previously Published Citation
Suggested citation
Janas, Michael. (2018). Applications of Semiclassical Theory in Statistical and Quantum Mechanics. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/200326.
Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.