2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215443We give a condition on a piecewise constant roof function and an irrational rotation by $α$ on the circle to give rise to a special flow having the mild mixing property. Such flows will also satisfy Ratner's property. As a consequence we obtain a class of mildly mixing singular flows on the two-torus that arise from quasi-periodic Hamiltonians flows by velocity changes.Accepted for publication in Discrete Contin. Dyn. SystDynamical Systems37A10, 37C40, 37E35text