Bounds for nonadiabatic transitions
Takuya Hatomura, Go Kato · Physical Review A · 2020
We discuss bounds for nonadiabatic transitions from the viewpoints of the adiabatic perturbation theory and the quantum speed limit. We show that the amount of nonadiabatic transitions from the $n\mathrm{th}$ level to the $m\mathrm{th}$ level is bounded by a function of the quantum geometric tensor for the $m\mathrm{th}$ level. We analyze this bound from the viewpoint of the adiabatic perturbation theory. In addition, this bound and the viewpoint of the quantum speed limit suggest a nontrivial relationship between the dynamical transformation and the adiabatic transformation. We also derive a universal bound for any nonadiabatic transition. This bound is written in terms of the counterdiabatic Hamiltonian.