Kibble-Zurek mechanism with a single particle: Dynamics of the localization-delocalization transition in the Aubry-André model
Kibble-Zurek mechanism with a single particle: Dynamics of the localization-delocalization transition in the Aubry-André model
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 …