  Quenches in isolated quantum systems are currently a subject of intense
study. Here, we consider quantum few-mode systems that are integrable in their
classical mean-field limit and become dynamically unstable after a quench of a
system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a
double-well potential and an antiferromagnetic spinor BEC constrained to a
single spatial mode. We study the time dynamics after the quench within the
truncated Wigner approximation (TWA) and find that system relaxes to a steady
state due to phase-space mixing. Using the action-angle formalism and a
pendulum as an illustration, we derive general analytical expressions for the
time evolution of expectation values of observables and their long-time limits.
We find that the deviation of the long-time expectation value from its
classical value scales as $1/O(\ln N )$, where $N$ is the number of atoms in
the condensate. Furthermore, the relaxation of an observable to its steady
state value is a damped oscillation and the damping is Gaussian in time. We
confirm our results with numerical TWA simulations.
