Equivalence of the Floquet–Magnus and Fer Expansions to Investigate the Dynamics of a Spin System in the Three-Level System

A critique on the suitability of Fer expansion in time-evolution studies in quantum mechanics

The present report examines the utility and exactness of time-propagators derived from Fer expansion (FE). While the mathematical intricacies of the FE scheme are well established, the operational aspects of the same in time-evolution studies remain less explored and authenticated in physical problems of relevance. Through suitable examples, the operational inconsistencies observed in time-evolution studies based on the FE scheme are identified and corroborated through rigorous comparisons with simulations emerging from exact numerical methods. The limitations outlined seriously undermine the advantages associated with the FE scheme over other existing analytic methods.