Statistically interacting quantum gases in D dimensions
Chapter 1. Exact and explicit results are derived for the thermodynamic properties (isochores, isotherms, isobars, response functions, speed of sound) of a quantum gas in dimensions D ≥ 1 and with fractional exclusion statistics 0 ≤ g ≤ 1 connecting bosons (g = 0) and fermions (g = 1). In D = 1 the results are equivalent to those of the Calogero-Sutherland model, a gas with long-range two-body interaction. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T-dependence of the speed of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential. ^ Chapter 2. The exact thermodynamics (isochores, isotherms, isobars, response functions, speed of sound) is worked out for a statistically interacting quantum gas in D dimensions. The results in D = 1 are those of the thermodynamic Bethe ansatz for the Nonlinear Schrödinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for D >> 1 and, in the limit D → ∞, a phase transition occurs at T > 0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite D .^ Chapter 3. Methodology previously developed in the framework of the coordinate Bethe ansatz applied to integrable quantum gas models is employed to calculate some ground-state properties and elementary excitations for quantum gas models in D = 1 dimensions with statistical interactions that are not equivalent to dynamical interactions. The focus in this comparative study is on modifications of the Calogero-Sutherland and Nonlinear Schrödinger models. Statistical interactions cannot be chosen arbitrarily. They must satisfy certain physicality conditions, which will be discussed in some detail. ^
Physics, Condensed Matter
Geoffrey G Potter,
"Statistically interacting quantum gases in D dimensions"
Dissertations and Master's Theses (Campus Access).