Yrast states of quantum droplets confined in a ring potential

We consider a quantum droplet which is confined in a ring potential. We investigate the so-called "yrast" state, i.e., the lowest-energy state of the droplet assuming that it has some fixed expectation value of the angular momentum. Two are the most interesting aspects of this problem, the nonlinear term -- which is partly attractive and partly repulsive -- and the periodic boundary conditions. For some range of the parameters, the attractive, or the repulsive part of the nonlinear term dominates and one gets the expected behavior. In some intermediate regime the two nonlinear terms are of comparable size. In this case both the solution, as well as the corresponding dispersion relation show an interesting behavior. Finally, we make contact with the problem of solitary-wave excitation, since the derived solutions are travelling-wave, i.e., solitary-wave, solutions.