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Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice


Müller, Hans-Michael (1999) Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yznz-2b69.


In the first part I perform Hartree-Fock calculations to show that quantum dots (i.e., two-dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. I tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wave function and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, I also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states and suggest an experimental method to detect Wigner crystals.

The second part of the thesis investigates infinite nuclear matter on a cubic lattice. The exact thermal formalism describes nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin-exchange and isospin-exchange interaction. Using auxiliary field Monte Carlo methods, I show that energy and basic saturation properties of nuclear matter can be reproduced. A first order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. The structure of the clusters is investigated with the help two-body correlations. I compare symmetry energy and first sound velocities with literature and find reasonable agreement. I also calculate the energy of pure neutron matter and search for a similar phase transition, but the survey is restricted by the infamous Monte Carlo sign problem. Also, a regularization scheme to extract potential parameters from scattering lengths and effective ranges is investigated.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Koonin, Steven E.
Thesis Committee:
  • Unknown, Unknown
Defense Date:5 May 1999
Record Number:CaltechTHESIS:12042013-111115672
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8037
Deposited By: Benjamin Perez
Deposited On:04 Dec 2013 19:34
Last Modified:09 Nov 2022 19:19

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