  The Aubry-Andr\'e 1D lattice model describes a particle hopping in a
pseudo-random potential. Depending on its strength $\lambda$, all eigenstates
are either localized ($\lambda>1$) or delocalized ($\lambda<1$). Near the
transition, the localization length diverges like $\xi\sim(\lambda-1)^{-\nu}$
with $\nu=1$. We show that when the particle is initially prepared in a
localized ground state and the potential strength is slowly ramped down across
the transition, then -- in analogy with the Kibble-Zurek mechanism -- it enters
the delocalized phase having finite localization length
$\hat\xi\sim\tau_Q^{\nu/(1+z\nu)}$. Here $\tau_Q$ is ramp/quench time and $z$
is a dynamical exponent. At $\lambda=1$ we determine $z\simeq2.37$ from the
power law scaling of energy gap with lattice size $L$. Even though for infinite
$L$ the model is gapless, we show that the gap relevant for excitation during
the ramp remains finite. Close to the critical point it scales like $\xi^{-z}$
with the value of $z$ determined by the finite size scaling. It is the gap
between the ground state and the lowest of those excited states that overlap
with the ground state enough to be accessible for excitation. We propose an
experiment with a non-interacting BEC to test our prediction. Our hypothesis is
further supported by considering a generalized version of Aubry-Andr\'{e} model
possessing an energy-dependent mobility edge.
