  A fully resolvable quantum many-body Hamiltonian is introduced that mimics
the behavior of the autocatalytic chemical reaction A+B <-> 2B involving two
different molecular species, A and B. The model also describes two
nonlinearly-coupled modes of an optical cavity. Consistent with the current
understanding of the relaxation dynamics of integrable systems in isolation,
the wavefunction following a quantum quench exhibits irreversibility with
retention of the memory about its initial conditions. Salient features of the
model include a marked similarity with conventional quantum decay and a total
B-to-A conversion, with associated classical-like behavior of the wavefunction,
when the initial state does not contain A-type molecules.
