Toward the correspondence between Q-clouds and sphalerons

Non-linear classical equations of motion may admit degenerate solutions at fixed charges. Whereas the solutions with lower energies are classically stable, those with larger energies are unstable and are referred to as Q-clouds. We consider a theory in which a homogeneous charged condensate is classically stable and argue that Q-clouds correspond to sphalerons between the stable Q-balls and the condensate. For a model with an analytical solution, we present the Arrhenius formula for the quantum production of Q-balls from a condensate at high temperatures