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COLD ATOMS AND THE CONFORMAL BOOTSTRAP

dc.contributor.authorSquires, Joshua
dc.contributor.chairLeclair, Andre Roger
dc.contributor.committeeMemberMueller, Erich
dc.contributor.committeeMemberNowack, Katja C.
dc.date.accessioned2019-10-15T16:47:39Z
dc.date.available2019-10-15T16:47:39Z
dc.date.issued2019-08-30
dc.description.abstractStatistical mechanics naturally lends itself to computational algorithms that use random sampling to leverage the law of large numbers. Though these methods have proven invaluable, in many cases yielding solutions to otherwise intractable problems, to an extent they also obscure the underlying physics. The two numerical methods studied in this thesis do not fit this description. The first, the conformal bootstrap, imposes symmetry constraints on the four-point correlation functions of a conformal field theory to restrict the spectrum of allowed scaling dimensions of a theory. A variation of the conformal bootstrap is implemented to treat two important non-unitary CFTs, percolation and the self-avoiding walk. The second involves a formalism which provides an integral equation with a kernel based on the two-body S-matrix. The solution of this integral equation represents a single particle's energy in the presence of interactions with the rest of a cold atom gas. The formalism is applied to Berezinskii-Kosterlitz-Thouless and upper branch phase transitions.
dc.identifier.doihttps://doi.org/10.7298/vvt1-jb31
dc.identifier.otherSquires_cornellgrad_0058F_11573
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:11573
dc.identifier.otherbibid: 11050508
dc.identifier.urihttps://hdl.handle.net/1813/67525
dc.language.isoen_US
dc.subjectStatistical physics
dc.subjectBKT Phase Transitions
dc.subjectConformal Bootstrap
dc.subjectConformal Field Theory
dc.subjectMathematical Physics
dc.subjectUltracold atomic gases
dc.subjectStatistical mechanics
dc.subjectTheoretical physics
dc.subjectQuantum physics
dc.titleCOLD ATOMS AND THE CONFORMAL BOOTSTRAP
dc.typedissertation or thesis
dcterms.licensehttps://hdl.handle.net/1813/59810
thesis.degree.disciplinePhysics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh.D., Physics

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