The thermodynamics of N bosons in a length L in one dimension, with repulsive delta-function interaction, is studied numerically for finite N, L. The results show the nature of finite-size corrections and how the thermodynamic limit is approached, and hopefully will be of some guidance in seeking the solution of a more general model.
Abstract In 1963, Lieb and Liniger solved exactly a one-dimensional model of bosons interacting by a repulsive δ -potential and calculated the ground state in the thermodynamic limit. In the present work, we extend this model to a potential of three δ -functions—one of them is repulsive and the other two are attractive—modeling some aspects of the interaction between atoms, and we present an approximate solution for a dilute gas. In this limit, for low energy states, the results are found to be reduced to the ones of an effective Lieb–Liniger model with an effective δ -function of strength c eff and the regime of stability is identified. This may shed light on some aspects of interacting bosons.