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Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results

Stefan Giller·Cezary Gonera
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Abstract

A method of fundamental solutions has been used to investigate transitions in two energy level systems with no level crossing in a real time. Compact formulas for transition probabilities have been found in their exact form as well as in their adiabatic limit. No interference effects resulting from many level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev. {\bf A44} 4280 (1991)) have been detected in either case. It is argued that these results of this work are incorrect. However, some effects of Berry's phases are confirmed.

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Stefan Giller, Cezary Gonera. 2001-01-11. Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results. https://doi.org/10.1103/physreva.63.052101

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