Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions

P. J. Forrester, N. E. Frankel, T. M. Garoni

The density matrix for the impenetrable Bose gas in Dirichlet and Neumann boundary conditions can be written in terms of $<{\prod }_{l=1}^n|\cos {\varphi }_1-\cos {\theta }_l||\cos {\varphi }_2-\cos {\theta }_l|>$, wher…