University of Illinois Urbana-Champaign

Classical hydrodynamics of Calogero-Sutherland models

Xing, Lei

Permalink

https://hdl.handle.net/2142/73044

Description

Title
Classical hydrodynamics of Calogero-Sutherland models
Author(s)
Xing, Lei
Issue Date
2015-01-21
Director of Research (if dissertation) or Advisor (if thesis)
Stone, Michael
Doctoral Committee Chair(s)
Stack, John
Committee Member(s)
  • Cooper, S. Lance
  • Peng, Jen-Chieh
  • Stone, Michael
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • spin
  • hydrodynamics
  • Calogero
  • soliton
  • integrability
Abstract
The Calogero Sutherland model is system of particle moving on a line and interacting with long-range forces. In this thesis we consider the classical case where the particles may or may not possess a spin degree of freedom. We demonstrate the intimate connection between the Calogero-Sutherland system and the Benjamin Ono equation. We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions. We show numerically that the spinful system also exhibits localized solutions with the soliton property. This is a strong evidence that the continuum spin-Calogero model is exactly integrable.
Graduation Semester
2014-12
Permalink
http://hdl.handle.net/2142/73044
Copyright and License Information
Copyright 2014 Lei Xing

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Physics
Dissertations in Physics