Date of Award

8-31-2017

Document Type

Campus Access Thesis

Degree Name

Master of Science (MS)

Department

Physics, Applied

First Advisor

Maxim Olchanyi

Second Advisor

Adolfo del Campo

Third Advisor

Steven Jackson

Abstract

The Bethe Ansatz is a quantum mechanics approach that ties together a rich literature of mapping quantum systems onto other problems and mathematical structures in order to gain exact solutions for their wave functions. In this thesis, we build on the work of such scientists as M. Gaudin and J. B. Mcguire of mapping one-dimensional gases onto systems of mirrors and constructing solutions based on the corresponding reflection groups, with their respective lowest degree anti-invariant polynomials representing the zero-energy state of the corresponding problem. Originally, these methods only allowed for mappings onto the crystallographic groups. However, with a particular coordinate transform, they can be extended to the non-crystallographic groups H3 and H4. The centerpiece of this thesis is a one-parametric family of mass-spectra for each of the two groups, with each family member leading to an exact solution for a particular system of impenetrable bosons. The zero-energy limit of these solutions, their usefulness for the study of entanglement, and the difficulty of extending them to penetrable particles is also discussed.

Comments

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