Numerical computation of dynamical Schwinger-like pair production in   graphene
  The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electrical field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the calculation is performed within the strong field quantum electrodynamics formalism, requiring a solution of the Dirac equation in momentum space. The latter is solved using a split-operator numerical scheme on parallel computers, allowing for the investigation of several field configurations. The strength of the method is illustrated by computing the electron momentum density generated from a realistic laser pulse model. We observe quantum interference patterns reminiscent of Landau-Zener-St\"{u}ckelberg interferometry. 
F. Fillion-Gourdeau, P. Blain, D. Gagnon, C. Lefebvre and S. MacLean
cond-mat.mes-hall quant-ph