Revisiting the applications of Floquet–Magnus and Fer expansion approaches in physics and solid-state NMR

Abstract

In this paper, we revisit, from different perspectives, the applications of Floquet–Magnus expansion (FME) and Fer expansion (FE) in NMR and physics. We use these expansion schemes for the calculation of effective Hamiltonians and propagators. We found that the FME is related to the FE. While both approaches are powerful methods, there are subtle differences between them. To understand the differences, we performed explicit calculation on various problems, namely, Bloch–Siegert shift, Cross Polarization (CP) and Continuous Waves (CW). We put the work in a prospect that is related to spin physics in order to make the calculation more general. As the propagator from the FME takes the form of the evolution operator, which removes the constraint of a stroboscopic observation, we appreciated the effects of time-evolution under Hamiltonians with different orders separately.