Theory of Nonadiabatic Transitions at Level-Crossing in Condensed Matter

Yōsuke Kayanuma

Frank Webster, Peter J. Rossky, Richard A. Friesner

N. A. Chigir

Hong Cao, Shao-Wu Yao, Li-Xiang Cen

Yoshiaki Teranishi, Hiroki Nakamura

A new idea of controlling nonadiabatic transitions by an external field is proposed. The basic principle is to periodically sweep an external field at each level crossing to make the overall transition probability from an initial state to any desirable final state equal to unity. The recently completed semiclassical theory of nonadiabatic transition enables us to analytically deal with this problem. The present idea may be applicable to various physical and chemical problems, whenever level crossings are created by an external field.

J. C. D’Olivo

The Magnus expansion of the time-displacement operator is used to calculate nonadiabatic level crossing induced by a time-dependent Hamiltonian. We consider Hamiltonians that can be represented as a Hermitian 2\ifmmode\times\else\texttimes\fi{}2 matrix. As an interesting nontrivial application an analytic expression for the flavor survival probability is derived for neutrinos which propagate through a matter-enhanced oscillation region.