Abstract
A semiclassical solution of general two-state non-adiabatic transition and tunneling is found analytically within the Wentzel–Kramers–Brillouin (WKB) semiclassical framework associated with the Stokes phenomenon in mathematics. The non-adiabatic scattering matrix is determined by a complex quantity called the Stokes constant, which can be directly connected to the complex transition points of the WKB solution. An accurate and compact analytical solution is found for this Stokes constant which is a function of three parameters, one of which corresponds to the diabatic-to-adiabatic transformation angle that is interpreted as a type of non-adiabatic transition. Numerical examples demonstrate that the present unified analytical semiclassical theory works very well for both non-adiabatic transition and non-adiabatic tunneling. The present analytical semiclassical method can be a very powerful tool for application to multidimensional non-adiabatic dynamic processes.
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