C. J. Pethick

GROUND-STATE PROPERTIES OF MAGNETICALLY TRAPPED BOSE-CONDENSED RUBIDIUM GAS

In light of the recent experimental observation of Bose-Einstein condensation in dilute

Landau Levels and the Thomas-Fermi Structure of Rapidly Rotating Bose-Einstein Condensates

{}^{87}mathrm{Rb}

Mobility of negative ions in superfluid 3He-B

gas cooled to nanokelvin-scale temperatures, we give a quantitative account of the ground-state properties of magnetically trapped Bose gases. Using simple scaling arguments, we show that at large particle number the kinetic energy is a small perturbation, and find a spatial structure of the cloud of atoms and its momentum distribution dependent in an essential way on particle interactions. We also estimate the superfluid coherence length and the critical angular velocity at which vortex lines become energetically favorable.

Multipair contributions to the spin response of nuclear matter

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: (i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope function, which gives rise to components in higher Landau levels; (ii) the LLL wave function with a nonuniform vortex lattice. From variational calculations, we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice. The predicted distortions of the lattice are small, but in accord with recent measurements at lower rates of rotation.

Mobility tensor of negative ions in superfluid 3He-A

We calculate the mobility of negative ions in superfluid 3He-B. We first derive the general formula for the mobility, and show that to a good approximation the scattering of quasiparticles from an ion may be treated as elastic, both in the superfluid for temperatures not too far below the transition temperature and also in the normal state. The scattering cross section in the superfluid is then calculated in terms of normal state properties; as we show, it is vital to include the effects of superfluid correlations on intermediate states in the scattering process. We find that for quasiparticles near the gap edge, the quasiparticle-ion scattering amplitude has a resonant behavior, and that as a result of interference among many partial waves, the differential scattering cross section is strongly peaked in the forward direction and reduced at larger angles, in much the same way as in diffraction. The transport cross section for such a quasiparticle is strongly reduced compared to that for a normal state quasiparticle, and the mobility is consequently strongly enhanced. Detailed calculations of the mobility which contain essentially no free parameters, agree well with the experimental data.

Structure of vortices in rotating Bose-Einstein condensates

When modelling the collapse of massive stars leading to supernova explosions and the cooling of neutron stars, understanding the microphysical processes, such as the interaction of neutrinos within a dense medium are of vital importance. The interaction of neutrinos with nucleons (neutrons and protons) is altered by the presence of the medium, compared to the same process with free nucleons. Neutrino scattering and production processes may be characterized in terms of the excitations that are created or destroyed in the nuclear medium. One way to analyse the effects of the medium is by using Landaus theory of normal Fermi liquids. This theory gives simple relationships between physical quantities such as the spin susceptibility or the response to a weak interaction probe in terms of Landau parameters, that are measures of the interaction between quasiparticles. One problem when using Landau Fermi liquid theory for nucleon matter is that the interaction has a tensor component. The tensor interaction does not conserve the total spin and, as a consequence, there are generally contributions to long-wavelength response functions from states that have more than one quasiparticle-quasihole pair in the intermediate state. Such contributions cannot be calculated in terms of Landau parameters alone, since in the usual formulation of Landau theory, only singlepair excitations are considered. In this thesis three problems are addressed. First, we obtain bounds on the contributions from more than one quasiparticle-quasihole pair by using sum-rule arguments. Second, we derive expressions for static response functions allowing for the tensor components of the interaction. We analyse which the most important effects are on the static response of nucleon matter, and find that the major contributions comes from renormalization of coupling constants and transitions to states with more than one quasiparticle-quasihole pair. Third, we show how contributions to the dynamical response coming from states containing two quasiparticle-quasihole pairs may be evaluated in terms of Landau theory if one allows for the effect of collisions in the Landau kinetic equation. We consider the case of asymmetric nuclear matter, and our work goes beyond earlier works in that they contain the effects of collisions in addition to those of the mean field.

Velocity of vortices in inhomogeneous Bose–Einstein condensates

The mobility tensor of negative ions in the A phase of superfluid 3He is calculated for temperatures close to Tc. In this regime the scattering of superfluid quasiparticles from an electron bubble is practically elastic and the mobility tensor is expressed in terms of momentum transfer cross sections for an ion at rest. These generalized transport cross sections are obtained from the quasiparticle-ion scattering T-matrix, which we evaluate in terms of the normal state scattering amplitude. The p-wave pairing correlations in the intermediate states result in important interference effects among all partial waves in the scattering process, and, in addition, for the low-energy quasiparticles they lead to resonant states below the gap edge. These phenomena modify the scattering amplitude in the superfluid in an essential way and the differential quasiparticle-ion cross section is found to display strongly anisotropic, energy-dependent variations on the scale of the superfluid energy gap. We find that, in contrast to simple approximations, for low quasiparticle energies the parallel and perpendicular momentum transfer cross sections are very different from one another. Close to Tc, the calculated mobility remains rather isotropic, but at lower temperatures the anisotropy is considerably larger than predicted by simple approximations for the cross section. The computed results are compared with the available measurements.

One-component Fermi-liquid theory and the properties of UPt3.

We calculate the structure of individual vortices in rotating Bose-Einstein condensates in a transverse harmonic trap. Making a Wigner-Seitz approximation for the unit cell of the vortex lattice, we derive the Gross-Pitaevskii equation for the condensate wave function in each cell of the lattice, including effects of varying coarse grained density. We calculate the Abrikosov parameter, the fractional core area, and the energy of individual cells.

Unusual transport effects in anisotropic superconductors

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the vortex velocity is a sum of the local superfluid velocity, plus a correction related to the density gradient near the vortex. A consequence is that in rapidly rotating, harmonically trapped Bose-Einstein condensates, unlike in the usual situation in slowly rotating condensates and in hydrodynamics, vortices do not move with the local fluid velocity. We indicate how Kelvins conservation of circulation theorem is compatible with the velocity of the vortex center being different from the local fluid velocity. Finally, we derive an exact wave function for a single vortex near the rotation axis in a weakly interacting system, from which we derive the vortex precession rate.