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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.
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10.1103/physrevlett.124.210604
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Family-Vicsek Scaling of Roughness Growth in a Strongly Interacting Bose Gas
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