dc.contributor.author How, Pyeton en_US dc.date.accessioned 2012-12-17T13:53:11Z dc.date.available 2012-12-17T13:53:11Z dc.date.issued 2011-08-31 en_US dc.identifier.other bibid: 7955523 dc.identifier.uri https://hdl.handle.net/1813/30772 dc.description.abstract A novel formalism of quantum statistical mechanics, based on the zero-temperature S-matrix of the quantum system, is presented in this thesis. In our new formalism, the lowest order approximation ("two-body approximation") corresponds to the exact resummation of all binary collision terms, and can be expressed as an integral equation reminiscent of the thermodynamic Bethe Ansatz (TBA). Two applications of this formalism are explored: the critical point of a weakly-interacting Bose gas in two dimensions, and the scaling behavior of quantum gases at the unitary limit in two and three spatial dimensions. We found that a weakly-interacting 2D Bose gas undergoes a superfluid transition at Tc [ALMOST EQUAL TO] 2[pi]n/[m log(2[pi]/mg )], where n is the number density, m the mass of a particle, and g the coupling. In the unitary limit where the coupling g diverges, the two-body kernel of our integral equation has simple forms in both two and three spatial dimensions, and we were able to solve the integral equation numerically. Various scaling functions in the unitary limit are defined (as functions of [MICRO SIGN]/T ) and computed from the numerical solutions. For bosons in three spatial dimensions, we present evidence that the gas undergoes 3 a strongly interacting version of Bose-Einstein condensation at n[lamda]T [ALMOST EQUAL TO] 1.3, where n is the number density and [lamda]T is the thermal wavelength. Finally, we look at the ratio of shear viscosity to entropy density [eta]/s of the unitary quantum gas, which has a conjectured lower bound of [eta]/s [GREATER-THAN OR EQUAL TO] /4[pi]kb based on the AdS/CFT correspondence of a strongly coupled Yang-Mills theory. en_US dc.language.iso en_US en_US dc.title The S-Matrix Formulation Of Quantum Statistical Mechanics, With Applications To Cold Quantum Gas en_US dc.type dissertation or thesis en_US thesis.degree.discipline Physics thesis.degree.grantor Cornell University en_US thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Physics dc.contributor.chair Leclair, Andre Roger en_US dc.contributor.committeeMember Mueller, Erich en_US dc.contributor.committeeMember Gruner, Sol Michael en_US
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