Semiclassical approach to time-dependent tunnelling

We present an exact time-dependent semiclassical formulation of the dynamics of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta$\end{document}-atom subjected to an oscillating electric field. Through a simple approximation the results of Ergenzinger's more intuitive analysis are obtained. We also comment on the important role played by the imaginary tunnelling time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t_{0}$\end{document}, which is quite distinct from the usual adiabatic tunnelling time.