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

TL;DR

This paper demonstrates that Family-Vicsek scaling, a fundamental law of surface roughness growth, can emerge in strongly interacting quantum Bose gases, linking classical surface physics with quantum many-body dynamics.

Contribution

It introduces a surface-height operator for quantum bosonic systems, revealing the emergence of Family-Vicsek scaling in a strongly interacting quantum context.

Findings

Family-Vicsek scaling appears in quantum Bose gases.

Surface-height operator enables experimental observation.

Scaling behavior is accessible with current ultracold atom experiments.

Abstract

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.