# The one-dimensional delta-function Bose gas in the finite-coupling regime

*Statistical Mechanics/Combinatorics Seminar*

*by Melissa Makin*

*Institution:*School of Physics, The University of Melbourne

*Date: Thu 16th November 2006*

*Time: 3:15 PM*

*Location: Room 213, Richard Berry Building, The University of Melbourne*

*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