Dickson, Matthew (2019) Interacting Boson gases and large deviation principles. PhD thesis, University of Warwick.

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Abstract

We consider probabilistic models for interacting bosons at a positive temperature in the thermodynamic limit with random particle density. The Loop Soup representation is a marked point process arising from the Feynman-Kac formula for the grand canonical partition function for a Bose gas, and the Cycle Count representation is in turn found by projecting onto the space of mark-type densities. Interacting versions of the Loop Soup and Cycle Count models are found by applying Varadhan-like arguments. Large deviation principles are found for a variety of interactions, which provide representation formulae for the thermodynamic limit of the pressure and a means to study Bose-Einstein condensation in these models.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Interacting boson models, Bose-Einstein gas, Bosons -- Mathematical models, Loop spaces, Bose-Einstein condensation
Official Date:	September 2019
Dates:	Date Event September 2019 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Adams, Stefan
Sponsors:	Engineering and Physical Sciences Research Council
Format of File:	pdf
Extent:	viii, 193 leaves
Language:	eng

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