We develop and apply meanfield methods to two systems of significant interest in cold atom physics. The first system, and the main subject of this thesis, is a gas of polarized dipoles, in which the particles have a long range anisotropic interaction. The second system is a toroidally trapped gas that interacts via short range interactions.
Dipolar gases: We develop accurate techniques for dipolar Bose and Fermi gases accounting for both direct and exchange interactions. We detail an efficient numerical implementation of the meanfield treatment.
We study the thermodynamic and the first and second order correlation properties of the system. We find that exchange interactions cause the correlation functions to be anisotropic in the low temperature regime. We also find that many uniform gas thermodynamic predictions, for which direct interaction effects vanish, are qualitatively unreliable for trapped systems, most notably for oblate traps.
Using Hartree-Fock theory and analytic approximations, we examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. The Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short range correlations between the particles we discuss the energetic origin of this difference.
Introducing local momentum distortion fields, we develop a practical Hartree-Fock theory in which exchange effects are described by a local effective potential. This theory is applicable at zero and finite temperature, and is in excellent agreement with full Hartree-Fock calculations.
Contact gases: We show how considerable simplification of numerical results and analytical derivations can be achieved in the local density approximation using a variety of density of states techniques.
We examine the process of isentropic loading of a Bose or Fermi gas from a harmonic trap into the scale invariant toroidal regime that exhibits a high degree of system invariance when increasing the radius of the toroid. For bosons a regime of cooling is identified and we find that the Fermi gas is subjected to irreducible heating during loading, caused by the loss of one degree of freedom for thermalization.
