Pallister, James 
ORCID: 0009-0004-0954-794X
(2024).
Limit shapes in one dimensional free fermion systems.
University of Birmingham.
Ph.D.
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Pallister2024PhD.pdf
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Abstract
In this thesis we study rare fluctuations in one dimensional free fermion systems which take the form of space-time disturbances known as limit shapes. Limit shapes have a long, rich history, but substantially less has been said on what happens when limit shapes meet. The expectation is that they should combine to create some new shape. This work deals with finding a rigorous way to find and characterise these \textit{limit shape
transitions}. We are able to make considerable progress by mapping the free fermions to a class of models known as Coulomb gas models which can be readily solved. These Coulomb gas models exhibit phase transitions that we show correspond to transitions in the underlying limit shapes. As an extension, we are able to classify the limit shapes we find in an industrial way and better understand their fluctuations. Further, we present simple physical arguments that suggest that our results will be valid even in the strongly interacting regime, i.e. when the fermions are no longer free.
| Type of Work: | Thesis (Doctorates > Ph.D.) | |||||||||
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| Award Type: | Doctorates > Ph.D. | |||||||||
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| Licence: | Creative Commons: Attribution-Noncommercial-No Derivative Works 4.0 | |||||||||
| College/Faculty: | Colleges > College of Engineering & Physical Sciences | |||||||||
| School or Department: | School of Physics and Astronomy | |||||||||
| Funders: | Engineering and Physical Sciences Research Council | |||||||||
| Subjects: | Q Science > QC Physics | |||||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/15306 |
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