  The nonlinear transport properties of the Mott insulator are discussed with
focus on the many-body Landau-Zener mechanism. After reviewing basic concepts
such as the non-adiabatic geometric phase and the Schwinger mechanism, we study
the decay of the insulating groundstate in strong electric fields using the
time-dependent density matrix renormalization group. A short comment on the
proposed mapping to the quantum walk model is added before discussing the
relevance of the theory to experimental results.
  This article is a draft of a book chapter of the book entitled "Quantum and
Semi-classical Percolation & Breakdown" (Lecture Note in Physics,
Springer-Verlag), to appear 2008.
