Transition probabilities in tangential avoided crossings: adiabatic vs. non-adiabatic regimes

In this talk, we investigate the asymptotic behavior of the transition probability for two-level avoided crossings under the limit where two parameters -adiabatic parameter and energy gap parameter- simultaneously tend to zero. 

This work extends our previous collaboration with M.Zerzeri where avoided crossings are generated by tangential intersections and obey a non-adiabatic regime.

We focus not only on the asymptotic expansion of transition probability but also on a quantum interference caused by multiple avoided crossings and a coexistence of distinct two-parameter regimes arising from different vanishing orders. 

This is a joint work with K.Higuchi.