The main work of this thesis involves the calculation, using the Bethe ansatz, of two of the signature quantities of the one-dimensional delta-function Bose gas. These are the density matrix and concomitantly its Fourier transform the occupation numbers, and the correlation function and concomitantly its Fourier transform the structure factor. The coefficient of the delta-function is called the coupling constant; these quantities are calculated in the finite-coupling regime, both expansions around zero coupling and infinite coupling are considered. Further to this, the density matrix in the infinite coupling limit, and its first order correction, is recast into Toeplitz determinant form. From this the occupation numbers are calculated up to 36 particles for the ground state and up to 26 particles for the first and second excited states. This data is used to fit the coefficients of an ansatz for the occupation numbers. The correlation function in the infinite coupling limit, and its first order correction, is recast into a form which is easy to calculate for any N, and is determined explicitly in the thermodynamic limit.
| Identifer | oai:union.ndltd.org:ADTP/245303 |
| Creators | Makin, Melissa I. |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Terms and Conditions: Copyright in works deposited in the University of Melbourne Eprints Repository (UMER) is retained by the copyright owner. The work may not be altered without permission from the copyright owner. Readers may only, download, print, and save electronic copies of whole works for their own personal non-commercial use. Any use that exceeds these limits requires permission from the copyright owner. Attribution is essential when quoting or paraphrasing from these works., Open Access |
Page generated in 0.002 seconds