A simple model for interacting Bosons in one dimensional and quasi-one dimensional systems

Interactions in Bose gas are usually modeled by a delta function potential (i.e., each pair of particles interacts only where the positions of the two particles coincide). This description ignores the range of interaction. We calculated the effects of the finite range of the interactions. Inspired by Van-der Waals potential, we proposed a one dimensional interaction potential of 3 delta functions, the central one is repulsive and the two peripheral ones are attractive. This model introduces a length scale for the interaction without giving up the mathematical simplicity of using delta functions. By generalizing the work of Lieb and Liniger, we found an exact Bethe-ansatz solution for the spectrum of N interacting Bosons moving on a ring and showed that the effect of interaction range might be crucial in some cases.  Joint work with Shmuel Fishman and Wolfgang Ketterle