Moser, Thomas (2018) Point Interactions in Systems of Fermions. PhD thesis, IST Austria.
Text
thesis.pdf  Published Version Available under License All rights reserved. [IST20181043v1+1] Download (831Kb) 

Archive
ThesisAll.zip Restricted to Repository staff only Available under License All rights reserved. [IST20181043v1+2] Download (1495Kb) 
Abstract
In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the pointinteracting model. By restricting the N + 1 system to a box we define a finite density model with point in teractions. In the context of this system we will discuss the energy change when introducing a pointinteracting impurity into a system of noninteracting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the noninteracting system.
Item Type:  Thesis (PhD) 

DOI:  10.15479/AT:ISTA:th_1043 
Subjects:  500 Science > 510 Mathematics 500 Science > 510 Mathematics > 515 Analysis 500 Science > 510 Mathematics > 519 Probabilities & applied mathematics 500 Science > 530 Physics 
Research Group:  Seiringer Group 
Depositing User:  Thomas Moser 
Date Deposited:  16 Oct 2018 09:23 
Last Modified:  16 Oct 2018 09:23 
URI:  https://repository.ist.ac.at/id/eprint/1043 
Actions (login required)
View Item 