Measurement catastrophe and ballistic spread of charge density with vanishing current

One of the features many-body quantum systems with Hilbert-space fragmentation is existence stationary states manifesting jamming. It was recently shown that these are "states memory", in which, e.g., measuring a localised observable has everlasting macroscopic effects. We study such measurement catastrophe an example stands out for its clarity. show particular at late times expectation value charge density becomes nontrivial function ratio between distance and time notwithstanding corresponding current approaching zero.