The one-dimensional delta-function Bose gas in the finite-coupling regime
by Melissa Makin
Abstract: An overview of a more intensive study of both the density matrix and the
occupation numbers of the one-dimensional delta-function Bose gas in the finite-coupling regime is presented. Specifically, the first two terms of the 1/cL expansion of the density matrix, where c is the coefficient of the two particle delta-function potential and L is the length of the system, are shown.
This work requires evaluation of the density matrix for a finite number of particles,
which is expressed in terms of multiple integrals. As multiple integrals are difficult to evaluate numerically, an alternative technique has been utilised whereby these expressions are converted to Toeplitz determinant form. Occupation numbers for the ground
state up to 36 particles, and for the first and second excited states up to 26 particles, are determined. Utilising these results, the coefficients of an ansatz for the general occupation numbers are presented.
For More Information: Dr. Iwan Jensen Phone: +61 3 8344 5214 I.Jensen@ms.unimelb.edu.au