报告摘要：

  We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schrodinger equations with periodic potentials. This is a prominent model in solid state physics and we also allow for perturbations by non-periodic potentials describing external electric fields. Our approach is based on the classical Bloch decomposition method which allows to diagonalize the periodic part of the Hamiltonian operator and treat the non-periodic potentials as a perturbation. This method proves to be superior to the mainly used time-splitting spectral schemes. Indeed it is shown by the given examples, that our method is unconditionally stable, highly efficient and allows for much larger time-steps than the traditional time-splitting schemes. To this end a particular focus is on the semiclassical regime, where the new algorithm naturally incorporates the adiabatic splitting of slow and fast scales.

报告时间： 2006年12月21日(周四) 下午4:00--5:00

报告地点：科技综合楼三层311报告厅