Many Body Topics in Condensed Matter Physics

Anduaga, Inaki P.

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

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

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

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

Copyright and License Information

Copyright 2010 Inaki P. Anduaga

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