On the equivalence between different averaging schemes in magnetic resonance

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.

A perspective on the relative merits/demerits of time-propagators based on Floquet theorem

The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem. Specifically, time-propagators of the form, U(t) = P(t)e-iH̄t defined in the Hilbert space (of finite dimension), are derived through generalized multimodal expansion of the operators involved. While Floquet methods defined in the extended Hilbert space (of infinite dimension) have remained the method of choice for the description of time-evolution at non-stroboscopic time-intervals, the expansion schemes discussed do present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods deserve formal validation in problems of experimental relevance. Employing examples comprising periodic Hamiltonians from magnetic resonance spectroscopy, the exactness of Floquet based time-propagators in the Schrödinger and interaction representation is discussed. Through rigorous comparisons between simulations emerging from analytic and exact numerical methods, the relative merits and demerits of different formulations of Floquet based methods are also discussed.

Theory of radio-frequency pulses on periodically driven three-level systems: challenges and perspectives

Nuances of multiple-quantum transitions in periodically driven systems is discussed through analytical methods based on time propagators derived from Floquet theory.

Bimodal Floquet theory of phase-modulated heteronuclear decoupling experiments in solid-state NMR spectroscopy

A prescription based on bimodal Floquet theory is proposed to describe the nuances of phase-modulated supercycled decoupling experiments in solids. The frequency dependent interaction frames relevant to a particular supercycle are identified to facilitate faster convergence of perturbation corrections to the derived effective Hamiltonians. In contrast to silico-based methods, the proposed analytic method offers an attractive platform for faster optimization of experiments in solids. Additionally, the relevance of supercycling at ultrafast spinning conditions is also discussed.