  Inspired by the recent results on totally asymmetric simple exclusion
processes on a periodic lattice with short-ranged quenched hopping rates [A.
Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study the universal
scaling properties of the Kardar-Parisi-Zhang (KPZ) equation with short-ranged
quenched columnar disorder in general d-dimensions. We show that there are
generic propagating modes in the system that have their origin in the quenched
disorder and make the system anisotropic. We argue that the presence of the
propagating modes actually make the effects of the quenched disorder
irrelevant, making the universal long wavelength scaling property belong to the
well-known KPZ universality class. On the other hand, when these waves vanish
in a special limit of the model, new universality class emerges with dimension
d = 4 as the lower critical dimension, above which the system is speculated to
admit a disorder-induced roughening transition to a perturbatively inaccessible
rough phase.
