University of Illinois Urbana-Champaign

Many Body Topics in Condensed Matter Physics

Anduaga, Inaki P.

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Anduaga_Inaki.pdf

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https://hdl.handle.net/2142/18225

Description

Title
Many Body Topics in Condensed Matter Physics
Author(s)
Anduaga, Inaki P.
Issue Date
2011-01-14T22:40:31Z
Director of Research (if dissertation) or Advisor (if thesis)
Stone, Michael
Doctoral Committee Chair(s)
Leigh, Robert G.
Committee Member(s)
  • Stone, Michael
  • Oono, Yoshitsugu
  • Greene, Laura H.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2011-01-14T22:40:31Z
Keyword(s)
  • Calogero Sutherland Model
  • Integrable systems
  • Helium 3 angular momentum paradox
  • p+ip superfluid angular momentum
Abstract
Two different problems involving many-body systems are presented. A hydrodynamic version of the Calogero system of one-dimensional particles interacting on the line is derived using a classical field formalism, and the results are contrasted to a derivation starting from first quantum mechanical principles. This new classical approach is shown to help in understanding subtleties occurring in the latter, such as the conditions for chiral motion, the decomposition of the Hamiltonian in terms of chiral currents and the nature of the physical velocity and density operators. Explicit collective solitonic excitations in the linear and non-linear limits are also presented. Additionally, we overview the possibility of expanding this formalism to the study of the Fractional Quantum Hall Effect. The second problem involves a simple two-dimensional model of a px + ipy superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubovde Gennes operator. The results confirm theoretical predictions such as the Thomas-Fermi approximation and the Ishikawa formula, in which the mass flow at zero-temperature and for a constant director l follows jmass = 1/2 curl(ρ hbar l/2).
Graduation Semester
2010-12
Permalink
http://hdl.handle.net/2142/18225
Copyright and License Information
Copyright 2010 Inaki P. Anduaga

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