Classical hydrodynamics of Calogero-Sutherland models

Xing, Lei

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

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

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

Copyright and License Information

Copyright 2014 Lei Xing

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