Exactly solvable toy model of autocatalysis: Irreversible relaxation after a quantum quench.

A 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 wave function 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 wave function, when the initial state does not contain A-type molecules.