Abstract
The impact of nonlinear interaction on the loop structure of lower energy level and on the time evolution curve of canonical momentum which corresponds to the lower eigenstate are analyzed respectively. We find that the curve changes from single-valued to multi-valued as nonlinear interaction grows. The fascinating part is that the time range delimited by turning points in the loop of energy level and the period between two inflexion points on the multi-valued part of the evolution curve of canonical momentum are the same. Therefore, we propose a characteristic time in the transition process of nonlinear Landau–Zener model in adiabatic limit. Last, the physical meaning of the transition time as a measure of how much time the system experiences a structural change which directly results in the breakdown of adiabaticity is discussed.
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