  The late-time dynamics of quantum many-body systems is organized in distinct
dynamical universality classes, characterized by their conservation laws and
thus by their emergent hydrodynamic transport. Here, we study transport in the
one-dimensional Hubbard model with different masses of the two fermionic
species. To this end, we develop a quantum Boltzmann approach valid in the
limit of weak interactions. We explore the crossover from ballistic to
diffusive transport, whose timescale strongly depends on the mass ratio of the
two species. For timescales accessible with matrix product operators, we find
excellent agreement between these numerically exact results and the quantum
Boltzmann equation, even for intermediate interactions. We investigate two
scenarios which have been recently studied with ultracold atom experiments.
First, in the presence of a tilt, the quantum Boltzmann equation predicts that
transport is significantly slowed down and becomes subdiffusive, consistent
with previous studies. Second, we study transport probed by displacing a
harmonic confinement potential and find good quantitative agreement with recent
experimental data [N. Darkwah Oppong et al., arXiv:2011.12411]. Our results
demonstrate that the quantum Boltzmann equation is a useful tool to study
complex non-equilibrium states in inhomogeneous potentials, as often probed
with synthetic quantum systems.
