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Gaps, Traps and Lattices - Correlations in Small Quantum Systems

Borgh, Magnus LU (2007)
Abstract (Swedish)
Popular Abstract in Swedish

I denna avhandling studeras egenskaper hos tvådimensionella, kvantmekaniska mångpartikelsystem. Studierna utförs med spinndensitetsfunktionalteori (SDFT) med den lokala spinndensitetsapproximationen (LSDA), samt med numerisk exakt diagonalisering. De egenskaper som studeras inkluderar symmetribrytande tillstånd i kvantprickar med få elektroner, gap i inneslutna fåpartikelsystem, magnetiska egenskaper hos kalla, fermioniska atomer i optiska gitter, och virvelbildning i fåpartikelsystem. I avhandlingen studeras också egenskaper hos SDFT-LSDA-metoden för mångpartikelberäkningar i sig.



Avhandlingen omfattar fem originalartiklar, vilka presenteras efter en introduktion till... (More)
Popular Abstract in Swedish

I denna avhandling studeras egenskaper hos tvådimensionella, kvantmekaniska mångpartikelsystem. Studierna utförs med spinndensitetsfunktionalteori (SDFT) med den lokala spinndensitetsapproximationen (LSDA), samt med numerisk exakt diagonalisering. De egenskaper som studeras inkluderar symmetribrytande tillstånd i kvantprickar med få elektroner, gap i inneslutna fåpartikelsystem, magnetiska egenskaper hos kalla, fermioniska atomer i optiska gitter, och virvelbildning i fåpartikelsystem. I avhandlingen studeras också egenskaper hos SDFT-LSDA-metoden för mångpartikelberäkningar i sig.



Avhandlingen omfattar fem originalartiklar, vilka presenteras efter en introduktion till forskningsområdena, till de metoder som används, och till de system som studeras.



Artikel I undersöker symmetribrytande tillstånd in kvantprickar, samt tillförlitligheten hos SDFT-LSDA för sådana system. Vi finner att SDFT-LSDA kan införa artificiella energiskillnader mellan de ingående tillstånden i en degenererad spinnmultiplett i grundtillståndet.



Artikel II undersöker tillförlitligheten hos SDFT-LSDA när metoden används för att beräkna gap samt partikeladditions- och partikelsubtraktionsenergier i fåelektronsystem. Vi finner att, i motsats till vad som gäller i atomer och utsträckta, fasta kroppar, Kohn-Sham-egenvärdena kan användas för att beräkna additions- och subtraktionsenergier i paraboliskt inneslutna system. Dessutom förutsäger vi i artikel II att system av kalla atomer uppvisar van der Waals-blockad, analogt med Coulomb-blockad i elektronsystem.



I artikel III respektive IV används medelfältsteori för att studera de magnetiska egenskaperna hos kalla, fermioniska atomer i ett optiskt gitter. Resultaten jämförs med en liknande studie för gitter av kvantprickar. Vi finner ett rikt magnetiskt fasdiagram, med icke-magnetiska, ferromagnetiska och antiferromagnetiska tillstånd. Fasdiagrammet för det optiska gittret uppvisar stora likheter med fasdiagrammet för kvantpricksgittret.



I artikel V används exakt diagonalisering för att studera virvelbildning i roterande fåpartikelsystem. Vi studerar system som består av Coulomb-växelverkande fermioner (elektroner), Coulomb-växelverkande bosoner, samt bosoner med växelverkan med kort räckvidd. Vi finner att virvelbildning i dessa system uppvisar universella egenskaper. (Less)
Abstract
This dissertation investigates properties of two-dimensional many-body systems. Studies are performed using the Spin-Density Functional Theory with the Local Spin-Density Approximation, and numerical exact diagonalization. The properties studied include symmetry-breaking states in few-electron quantum dots, gaps in confined few-body systems, magnetic properties of cold fermionic atoms in optical lattices, and vortex formation in few-body systems. The dissertation also studies the properties of the SDFT-LSDA method for many-body calculations itself.



The dissertation comprises five original papers, which are presented following an introduction to the fields of research, and the methods used, and the systems... (More)
This dissertation investigates properties of two-dimensional many-body systems. Studies are performed using the Spin-Density Functional Theory with the Local Spin-Density Approximation, and numerical exact diagonalization. The properties studied include symmetry-breaking states in few-electron quantum dots, gaps in confined few-body systems, magnetic properties of cold fermionic atoms in optical lattices, and vortex formation in few-body systems. The dissertation also studies the properties of the SDFT-LSDA method for many-body calculations itself.



The dissertation comprises five original papers, which are presented following an introduction to the fields of research, and the methods used, and the systems studied.



Paper I investigates symmetry-breaking states in quantum dots, and the reliability of SDFT-LSDA for such systems. It is found that SDFT-LSDA may introduce artificial energy splittings between the members of a degenerate spin multiplet in the ground state.



Paper II investigates the reliability of SDFT-LSDA when used to calculate gaps, and addition and removal energies in few-body systems. It is found that, contrary to studies of atoms and bilk solids, Kohn-Sham eigenvalues can be used to calculate addition and removal energies in parabolically confined systems. Also, in Paper II, van der Waals blockade is predicted to occur in systems of cold atoms, in analogy to Coulomb blockade in electronic systems.



In Papers III and IV, mean-field theory is used to study the magnetic properties of cold fermionic atoms in an optical lattice. The results are compared with a similar study for quantum-dot lattices. It is found that there is a rich magnetic phase diagram, with non-magnetic, ferromagnetic, and anti-ferromagnetic states. The phase diagram of the optical lattice is found to be very similar to the phase diagram of the quantum-dot lattice.



Paper V uses exact diagonalization to study vortex formation in rotating few-body quantum systems. Systems consisting of Coulomb-interacting fermions (electrons), Coulomb-interacting bosons, and bosons with a short-range interaction are studied. It is found that vortex formation in these systems has universal properties. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Guðmundsson, Viðar, Department of Physics, Faculty of Science, University of Iceland, Iceland.
organization
publishing date
type
Thesis
publication status
published
subject
keywords
magnetiska och optiska), egenskaper (elektriska, Cold atoms, Quantum dots, Optical lattices, classical mechanics, Mathematical and general theoretical physics, Exact diagonalization, Density Functional Theory, Vortices, relativity, quantum mechanics, termodynamik, statistisk fysik, relativitet, kvantmekanik, klassisk mekanik, Matematisk och allmän teoretisk fysik, thermodynamics, statistical physics, Condensed matter:electronic structure, gravitation, supraledare, magnetisk resonans, electrical, magnetic and optical properties, supraconductors, magnetic resonance, relaxation, spectroscopy, Kondenserade materiens egenskaper:elektronstruktur, spektroskopi, Fysicumarkivet A:2007:Borgh
pages
158 pages
publisher
Division of Mathematical Physics, Department of Physics, Faculty of Engineering, Lund University
defense location
Lecture hall F, Department of Physics, Sölvegatan 14A Lund University Faculty of Engineering
defense date
2007-04-27 10:15
ISBN
978-91-628-7134-5
language
English
LU publication?
yes
id
d6bdd549-7a96-493d-a434-f58c89c2c6e7 (old id 548399)
date added to LUP
2007-09-28 09:38:52
date last changed
2016-09-19 08:45:06
@misc{d6bdd549-7a96-493d-a434-f58c89c2c6e7,
  abstract     = {This dissertation investigates properties of two-dimensional many-body systems. Studies are performed using the Spin-Density Functional Theory with the Local Spin-Density Approximation, and numerical exact diagonalization. The properties studied include symmetry-breaking states in few-electron quantum dots, gaps in confined few-body systems, magnetic properties of cold fermionic atoms in optical lattices, and vortex formation in few-body systems. The dissertation also studies the properties of the SDFT-LSDA method for many-body calculations itself.<br/><br>
<br/><br>
The dissertation comprises five original papers, which are presented following an introduction to the fields of research, and the methods used, and the systems studied.<br/><br>
<br/><br>
Paper I investigates symmetry-breaking states in quantum dots, and the reliability of SDFT-LSDA for such systems. It is found that SDFT-LSDA may introduce artificial energy splittings between the members of a degenerate spin multiplet in the ground state.<br/><br>
<br/><br>
Paper II investigates the reliability of SDFT-LSDA when used to calculate gaps, and addition and removal energies in few-body systems. It is found that, contrary to studies of atoms and bilk solids, Kohn-Sham eigenvalues can be used to calculate addition and removal energies in parabolically confined systems. Also, in Paper II, van der Waals blockade is predicted to occur in systems of cold atoms, in analogy to Coulomb blockade in electronic systems.<br/><br>
<br/><br>
In Papers III and IV, mean-field theory is used to study the magnetic properties of cold fermionic atoms in an optical lattice. The results are compared with a similar study for quantum-dot lattices. It is found that there is a rich magnetic phase diagram, with non-magnetic, ferromagnetic, and anti-ferromagnetic states. The phase diagram of the optical lattice is found to be very similar to the phase diagram of the quantum-dot lattice.<br/><br>
<br/><br>
Paper V uses exact diagonalization to study vortex formation in rotating few-body quantum systems. Systems consisting of Coulomb-interacting fermions (electrons), Coulomb-interacting bosons, and bosons with a short-range interaction are studied. It is found that vortex formation in these systems has universal properties.},
  author       = {Borgh, Magnus},
  isbn         = {978-91-628-7134-5},
  keyword      = {magnetiska och optiska),egenskaper (elektriska,Cold atoms,Quantum dots,Optical lattices,classical mechanics,Mathematical and general theoretical physics,Exact diagonalization,Density Functional Theory,Vortices,relativity,quantum mechanics,termodynamik,statistisk fysik,relativitet,kvantmekanik,klassisk mekanik,Matematisk och allmän teoretisk fysik,thermodynamics,statistical physics,Condensed matter:electronic structure,gravitation,supraledare,magnetisk resonans,electrical,magnetic and optical properties,supraconductors,magnetic resonance,relaxation,spectroscopy,Kondenserade materiens egenskaper:elektronstruktur,spektroskopi,Fysicumarkivet A:2007:Borgh},
  language     = {eng},
  pages        = {158},
  publisher    = {ARRAY(0x8979ed0)},
  title        = {Gaps, Traps and Lattices - Correlations in Small Quantum Systems},
  year         = {2007},
}