Crystallization waves (in memory of Alexander Parshin)

Melting-freezing wave is a peculiar phenomenon taking place on a surface of quantum crystal. This wave can propagate due to the extremely fast growth dynamics of the suface and due to the non-dissipative mass transport provided by the superfluid surrounding a crystal. This short paper reviews the studies of crystallization waves starting from their theoretical prediction and the first experimental observation by Alexander Parshin and his collegues.