Classical hydrodynamics of Calogero-Sutherland models

spin;hydrodynamics;Calogero;soliton;integrability

Xing, Lei

关键词: spin;    hydrodynamics;    Calogero;    soliton;    integrability;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/73044/Lei_Xing.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The Calogero Sutherland model is system of particle moving on a line and interacting with long-rangeforces. 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. Thisis a strong evidence that the continuum spin-Calogero model is exactly integrable.