  We consider the unitary dynamics of interacting fermions in the lowest Landau
level, on spherical and toroidal geometries. The dynamics are driven by the
interaction Hamiltonian which, viewed in the basis of single-particle Landau
orbitals, contains correlated pair hopping terms in addition to static
repulsion. This setting and this type of Hamiltonian has a significant history
in numerical studies of fractional quantum Hall (FQH) physics, but the
many-body quantum dynamics generated by such correlated hopping has not been
explored in detail. We focus on initial states containing all the fermions in
one block of orbitals. We characterize in detail how the fermionic liquid
spreads out starting from such a state. We identify and explain differences
with regular (single-particle) hopping Hamiltonians. Such differences are seen,
e.g. in the entanglement dynamics, in that some initial block states are frozen
or near-frozen, and in density gradients persisting in long-time equilibrated
states. Examining the level spacing statistics, we show that the most common
Hamiltonians used in FQH physics are not integrable, and explain that GOE
statistics (level statistics corresponding to the Gaussian Orthogonal Ensemble)
can appear in many cases despite the lack of time-reversal symmetry.
