Journal of Mathematical Physics

On the Landau–Zener formula for two-level systems

Vojkan Jakšić, Jan Segert

Published Jul 1, 1993• 14 citations

Abstract

It is shown that the transition probability between eigenstates of a time-dependent two-level system is given by the Fourier transform in the adiabatic parameter of a function determined by the Hamiltonian. Sufficient and necessary conditions for the transition probability between levels to decrease exponentially in the adiabatic limit are established. Our method involves a Paley–Wiener type theorem to study the Fourier transform of functions belonging to a Hardy class on a strip.

DOI: 10.1063/1.530097

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