In English

Tunneling Theory for Few-Body Systems in One-Dimensional Traps

Rikard Lundmark
Göteborg : Chalmers tekniska högskola, 2014. 75 s.
[Examensarbete på avancerad nivå]

In recent experiments, carried out at the University of Heidelberg, tunneling rates of ultracold distinguishable fermions out of an optomagnetical trap have been measured. The fermions interact by a tunable short-ranged interaction, and the trap is asymmetric making the trapped quantum system effectively one-dimensional. In this thesis, a method for calculating the energy levels and tunneling rates of one and two interacting particles out of a very general onedimensional potential well is devised. The method is based on expanding the Schrodinger equation of the system in a complex-momentum basis. This is done utilizing the so-called Berggren completeness relation. Ultimately, the basis expansion leads to a complex symmetric non-Hermitian eigenvalue problem for a large, dense matrix. The general method is applied to a system of trapped, ultracold fermionic atoms in a setup that closely resembles the Heidelberg experiments. The short-ranged interaction is modeled as a point-interaction, and the trap potential is regularized at large distances from the interesting region. The obtained energies and decay rates are contrasted to results obtained using the Wentzel-Kramers-Brillouin (WKB) approximation. Notable differences can be observed, and these may be due to insufficiency of the WKB approximation to accurately describe the system in question.



Publikationen registrerades 2014-05-07. Den ändrades senast 2015-07-28

CPL ID: 197684

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