Family-Vicsek Scaling of Roughness Growth in a Strongly Interacting Bose Gas

Family-Vicsek scaling is one of the most essential scale-invariant laws emerging in surface-roughness growth of classical systems. In this Letter, we theoretically elucidate the emergence of the Family-Vicsek scaling even in a strongly interacting quantum bosonic system by introducing a surface-height operator. This operator is comprised of a summation of local particle-number operators at a simultaneous time, and thus the observation of the surface roughness in the quantum many-body system and its scaling behavior are accessible to current experiments of ultracold atoms.