Analytical and Numerical Developments in Strongly Correlated Systems: Perspectives from TDDFT and Green's Functions

Research output: ThesisDoctoral Thesis (compilation)

Abstract

This thesis investigates different methods for treating strongly correlated systems, and discusses their respective strengths and weaknesses. Many of the results presented in this thesis come from comparing the different methods and approximations to exact results.
Paper I: We studied the real-time dynamics of a trapped fermion gas, as it expands after removal of a trapping potential.
Paper II: We constructed a new exchange-correlation potential, to be used in three dimensions. The potential is non-perturbative in the interaction, meaning that we could use it both for weakly interacting (metallic) systems, as well as for strongly interacting (Mott insulating) systems.
Paper III: We studied transport of electrons through small disordered wires contacted to leads. Using TDDFT, we have studied how the inclusion of both disorder and large electron-electron interactions affect conduction. At finite bias, we saw that the effects where competitive, and that interactions could increase the current through disordered samples.
Paper IV: We studied fermions in 3D, using our newly developed exchange-correlation potentials, presented in Paper II. We studied how a cloud of fermions expands when released from a trapping potential. The simulated systems were large enough to be relevant for actual experimental conditions.
Paper V: We studied transport of electrons through small disordered wires contacted to leads. The setup was similar to the one in Paper III, but another method was used - NEGF. Many of the observed trends were similar to those seen in our previous investigations. The differences were attributed to non-local effects.

Details

Authors
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Condensed Matter Physics

Keywords

  • Many-Body Perturbation Theory, Hubbard model, TDDFT, Green's function, DFT, Quantum Transport, Disorder, Fysicumarkivet A:2014:Karlsson
Original languageEnglish
QualificationDoctor
Awarding Institution
Supervisors/Assistant supervisor
Award date2014 Jun 4
Publisher
  • Division of Mathematical Physics, Faculty of Science, Lund University
Print ISBNs9789174739817
Publication statusPublished - 2014
Publication categoryResearch

Bibliographic note

Defence details Date: 2014-06-04 Time: 13:15 Place: Rydbergssalen, Sölvegatan 14A, Lund. External reviewer(s) Name: van Leeuwen, Robert Title: Prof. Affiliation: Department of Physics, Nanoscience Center, University of Jyväskylä, Survontie 9, 40014 Jyväskylä, ---

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