  Time-dependent driving of quantum systems has emerged as a powerful tool to
engineer exotic phases far from thermal equilibrium, but in the presence of
many-body interactions it also leads to runaway heating, so that generic
systems are believed to heat up until they reach a featureless
infinite-temperature state. Understanding the mechanisms by which such a heat
death can be slowed down or even avoided is a major goal -- one such mechanism
is to drive toward an even distribution of electrons in momentum space. Here we
show how such a mechanism avoids runaway heating for an interacting
charge-density-wave chain with a macroscopic number of conserved quantities
when driven by a strong dc electric field; minibands with nontrivial
distribution functions develop as the current is prematurely driven to zero.
Moreover, when approaching a zero-temperature resonance, the field strength can
tune between positive, negative, or close-to-infinite effective temperatures
for each miniband. Our results suggest that nontrivial metastable distribution
functions should be realized in the prethermal regime of quantum systems
coupled to slow bosonic modes.
