States of one-dimensional Coulomb systems as simple examples of θ vacua and confinement

The one-dimensional Coulomb system is known to have equilibrium states with nonvanishing electric field. These states are shown here to be analogous, and related, to the θ vacua which have been discussed for gauge theories in two or more space-time dimensions. The system exhibits confinement of fractional charges, which we dicuss with the purpose of offering a simple example of the θ-vacua phenomenology. Precise relations and connections between one-dimensional Coulomb gases and two-dimensional Abelian gauge theories, and quantum-mechanical matter systems, are discussed.