  We study energy transport in a chain of quantum harmonic and anharmonic
oscillators where the anharmonicity is induced by interaction between local
vibrational states of the chain. Using adiabatic elimination and numerical
simulations with matrix product states, we show how strong interactions
significantly slow down the relaxation dynamics (with the emergence of a new
time scale) and can alter the properties of the steady state. We also show that
steady state properties are completely different depending on the order in
which the limits of infinite time and infinite interaction are taken.
