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- W2001234413 abstract "The Landau-Zener-Stuckelberg-Majorana (LZSM) model is widely used for estimating transition probabilities in the presence of crossing energy levels in quantum physics. This model, however, makes the unphysical assumption of an infinitely long constant interaction, which introduces a divergent phase in the propagator. This divergence remains hidden when estimating output probabilities for a single input state insofar as the divergent phase cancels out. In this paper we show that, because of this divergent phase, the LZSM model is inadequate to describe the evolution of pure or mixed superposition states across a level crossing. The LZSM model can be used only if the system is initially in a single state or in a completely mixed superposition state. To this end, we show that the more realistic Demkov-Kunike model, which assumes a hyperbolic-tangent level crossing and a hyperbolic-secant interaction envelope, is free of divergences and is a much more adequate tool for describing the evolution through a level crossing for an arbitrary input state. For multiple crossing energies which are reducible to one or more effective two-state systems (e.g., by the Majorana and Morris-Shore decompositions), similar conclusions apply: the LZSM model does not produce definite values of the populations and the coherences, and one should use the Demkov-Kunike model instead." @default.
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- W2001234413 date "2011-12-09" @default.
- W2001234413 modified "2023-09-27" @default.
- W2001234413 title "Evolution of superpositions of quantum states through a level crossing" @default.
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- W2001234413 doi "https://doi.org/10.1103/physreva.84.063411" @default.
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