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

Examensarbete för masterexamen

Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12380/197684
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Type: Examensarbete för masterexamen
Master Thesis
Title: Tunneling Theory for Few-Body Systems in One-Dimensional Traps
Authors: Lundmark, Rikard
Abstract: 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 Schr odinger 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.
Keywords: Grundläggande vetenskaper;Fysik;Subatomär fysik;Kärnfysik;Lågenergifysik;Atomfysik;Lågtemperaturfysik;Beräkningsfysik;Basic Sciences;Physical Sciences;Subatomic Physics;Nuclear physics;Low energy physics;Atomic physics;Low temperature physics;Computational physics
Issue Date: 2014
Publisher: Chalmers tekniska högskola / Institutionen för fundamental fysik
Chalmers University of Technology / Department of Fundamental Physics
URI: https://hdl.handle.net/20.500.12380/197684
Collection:Examensarbeten för masterexamen // Master Theses



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