Novel Physics in the Calogero-Sutherland Model

Dasgupta, Abhishek (2011) Novel Physics in the Calogero-Sutherland Model. Masters thesis, Indian Institute of Science Education and Research-Kolkata.

PDF (MS Dissertation of Abhishek Dasgupta) AbhishekDasgupta_MSthesis-colour.pdf - Submitted Version Restricted to Repository staff only Download (511kB)

Abstract

Chapter 1 introduces the reader to the topic of the thesis, which is the novel physics that can be found in the Calogero-Sutherland-Moser model (CSM). A description of the rich physics and mathematics connected to this model is given and the focus areas of supersolidity and band structure are introduced, with references to prior literature in the subject. A brief introduction to supersolidity is given. Chapter 2 gives an outline of CSM, which is essentially a one-dimensional model with pairwise inverse square interactions between particles, together with a harmonic confinement. The energy eigenvalues and form of the wavefunctions are derived. Chapter 3 describes supersolidity in the CSM. The notion of off-diagonal long range order and diagonal long-range order, along with pair correlation functions are introduced and used to characterise supersolidity in the CSM. Numerical results based on Monte Carlo calculations are presented. Chapter 4 deals with band structure and fractional statistics in the CSM. Extending prior work in the field, we show a relation between the original, discrete, CSM solution and the band structure. Pair correlations are studied to elucidate the model. Initial progress is made in extending the band structure model, which was for three particles, to four particles. Chapter 5 concludes the thesis with a summary of the work. Possible future work, in both the supersolidity and band structure aspects, is described, which follows naturally from the work presented here.

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