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

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