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Via the hierarchy of correlations, we study the strongly interacting Fermi-Hubbard model in the Mott insulator state and couple it to a Markovian environment that constantly monitors the particle numbers { \^{}n}_^ and { \^{}n}_^ for each lattice site. As expected, the environment induces an imaginary part (i. e. , the decay rate) of the quasiparticle frequencies ₊₊-i, and it tends to diminish the correlations between lattice sites. Surprisingly, the environment also steers the state of the system on intermediate timescales O (1/) to a prerelaxed state very similar to the prethermalized state after a quantum quench (i. e. , suddenly switching on the hopping rate J). Full relaxation or thermalization occurs via local on-site heating and takes much longer.
Queißer et al. (Wed,) studied this question.