Correlation Functions of the One-Dimensional Attractive Bose Gas

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with a delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for a large number of particles, analogous to the Mössbauer effect.

Figure 1

Contribution to the DSF coming from $N-1:1$ (two-particle) states, in the large $N$ limit for $g=1$. The square-root singularity at the lower threshold is accompanied by a maximum around $k=[\omega -g^2/4{]}^{1/2}$.

Figure 2

Fixed momentum cuts of Fig. 1, showing the weakening of the square-root singularity at higher momentum, and the displacement of the maximum towards higher energies.