| dc.description.abstract | In this thesis I present a nonequilibrium quantum field theory that describes the
production of molecular dimers from a two-component quantum-degenerate atomic
Fermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach
resonance. This problem raises interest because it is presently unclear as to why
deviations from the universal Landau-Zener formula for the transition probability at
two-level crossing are observed in the experimentally measured production efficiencies.
The approach is based on evaluating real-time Green functions within the Keldysh-
Schwinger formalism. The effects of quantum statistics associated with Pauli blocking
for fermions and induced emission for bosons, characteristic of particle scattering in
a quantum-degenerate many-body medium, are fully accounted for. I show that the
molecular conversion efficiency is represented by a power series in terms of a dimensionless
parameter which, in the zero-temperature limit, depends solely on the initial
gas density and the Landau-Zener parameter. This result reveals a hindrance of the
canonical Landau-Zener transition probability due to many-body effects, and presents
an explanation for the experimentally observed deviations.
A second topic treated in this thesis concerns the study of non-adiabatic transitions
in N-state Landau-Zener systems. In connection to this, I provide a proof of
the conjecture put forth by Brundobler and Elser, regarding the survival probability
on the diabatic levels with maximum/minimum slope. | en |
