Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron   System
  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. 
Takashi Oka and Hideo Aoki