thesis
Point interactions in systems of fermions
ISTA Thesis
published
Thomas
Moser
author 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
Robert
Seiringer
supervisor
RoSe
department
Structure of the Excitation Spectrum for Many-Body Quantum Systems
project
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 point-interacting 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 point-interacting impurity into a system of non-interacting 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 non-interacting system.
https://research-explorer.ista.ac.at/download/52/6256/2018_Thesis_Moser.pdf
application/pdfno
https://research-explorer.ista.ac.at/download/52/6257/2018_Thesis_Moser_Source.zip
application/zip
Institute of Science and Technology Austria2018
eng
2663-337X10.15479/AT:ISTA:th_1043
115
https://research-explorer.ista.ac.at/record/5856 https://research-explorer.ista.ac.at/record/154 https://research-explorer.ista.ac.at/record/1198 https://research-explorer.ista.ac.at/record/741
T. Moser, “Point interactions in systems of fermions,” Institute of Science and Technology Austria, 2018.
Moser T. 2018. Point interactions in systems of fermions. Institute of Science and Technology Austria.
T. Moser, Point Interactions in Systems of Fermions, Institute of Science and Technology Austria, 2018.
Moser T. Point interactions in systems of fermions. 2018. doi:<a href="https://doi.org/10.15479/AT:ISTA:th_1043">10.15479/AT:ISTA:th_1043</a>
Moser, Thomas. “Point Interactions in Systems of Fermions.” Institute of Science and Technology Austria, 2018. <a href="https://doi.org/10.15479/AT:ISTA:th_1043">https://doi.org/10.15479/AT:ISTA:th_1043</a>.
Moser, Thomas. <i>Point Interactions in Systems of Fermions</i>. Institute of Science and Technology Austria, 2018, doi:<a href="https://doi.org/10.15479/AT:ISTA:th_1043">10.15479/AT:ISTA:th_1043</a>.
Moser, T. (2018). <i>Point interactions in systems of fermions</i>. Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/AT:ISTA:th_1043">https://doi.org/10.15479/AT:ISTA:th_1043</a>
522018-12-11T11:44:22Z2023-09-27T12:34:14Z