  Recent experimental and theoretical works have uncovered nontrivial quantum
dynamics due to external dissipation. Using an exact numerical method and a
renormalization-group-based analytical technique, we theoretically elucidate
that dissipation drastically alters universal particle-number-fluctuation
dynamics related to surface-roughness growth in non-interacting fermions and
bosons. In a system under dephasing that causes loss of spatial coherence, we
find that a universality class of surface-roughness dynamics changes from the
ballistic class to a class with the Edwards-Wilkinson scaling exponents and an
unconventional scaling function. On the other hand, in a system under
dissipation with in- and out-flow of particles that breaks particle-number
conservation, the universal dynamics is lost.
