  We study the out-of-equilibrium dynamics of a dilute, lattice-confined
Bose-Fermi mixture initialized in a highly excited state consisting of
boson-fermion pairs (doublons) occupying single lattice sites. This system
represents a paradigmatic case for studying relaxation dynamics in strongly
correlated systems, and provides a versatile platform for studying
thermalization and localization phenomena. We provide analytical expressions
for the short-time decay of isolated doublons and small doublon clusters due to
the competition between tunneling and interparticle interactions. We also
discuss a mechanism for long-time decay that crucially depends on the quantum
statistics of the particles constituting the doublon, namely, the conversion of
pairs of neighboring doublons into an unpaired fermion and a site with a
fermion and two bosons. Building on these insights, we develop a cluster
expansion method to describe the dynamics in extended systems and compare it to
numerically exact matrix product state simulations in one dimension. Finally,
we discuss how our predictions can be observed in experiments with ultracold
heteronuclear molecules.
