This dissertation discusses the Landau-Zener (LZ) theory and its application in
noisy environments and in many-body systems. The first project considers the effect
of fast quantum noise on LZ transitions. There are two important time intervals
separated by the characteristic LZ time. For each interval we derive and solve the
evolution equation, and match the solutions at the boundaries to get a complete
solution. Outside the LZ time interval, we derive the master equation, which differs
from the classical equation by a quantum commutation term. Inside the LZ time
interval, the mixed longitudinal-transverse noise correlation renormalizes the LZ gap
and the system evolves according to the renormalized LZ gap. In the extreme quantum
regime at zero temperature our theory gives a beautiful result which coincides
with that of other authors. Our initial attempts to solve two experimental puzzles
- an isotope effect and the quantized hysteresis curve of a single molecular magnet -
are also discussed.
The second project considers an ultracold dilute Fermi gas in a magnetic field
sweeping across the broad Feshbach resonance. The broad resonance condition allows
us to use the single mode approximation and to neglect the energy dispersion of the
fermions. We then propose the Global Spin Model Hamiltonian, whose ground state
we solve exactly, which yields the static limit properties of the BEC-BCS crossover. We also study the dynamics of the Global Spin Model by converting it to a LZ
problem. The resulting molecular production from the initial fermions is described
by a LZ-like formula with a strongly renormalized LZ gap that is independent of the
initial fermion density. We predict that molecular production during a field-sweep
strongly depends on the initial value of magnetic field. We predict that in the inverse
process of molecular dissociation, immediately after the sweeping stops there appear
Cooper pairs with parallel electronic spins and opposite momenta.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-05-773 |
| Date | 16 January 2010 |
| Creators | Sun, Deqiang |
| Contributors | Pokrovsky, Valery L. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation |
| Format | application/pdf |
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