The gauge coupled two-body problem in a ring

We study the properties of two quantum particles which are confined in a ring. The particles interact via a long-range gauge potential proportional to the distance between the particles. It is found that the two-body ground state corresponds to a state with non-zero angular momentum provided that the interaction between the particles is strong enough. In addition, the particles are correlated in the sense that depending on the interaction strength there is a propensity to be found close together or separated in the ring. We discuss the effect of measuring the position of one of the particles and thereby removing the particle from the ring, where we show that the remaining particle can be prepared in a non-dispersive state with non-zero angular momentum.