Duality in potential curve crossing: Application to quantum coherence

A field-dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve crossing. It is pointed out that weak and strong potential curve crossing interactions are interchanged under this transformation, thus realizing a naive strong and weak duality. A reliable perturbation theory should thus be formulated in limits of both weak and strong interactions. In fact, the main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well described by simple (time-independent) perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double-well potential is generally suppressed by the effect of a potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.