On the Floquet–Magnus expansion: Applications in solid-state nuclear magnetic resonance and physics

Abstract

Theoretical approaches are useful and powerful tools for more accurate and efficient spin dynamics simulation to understand experiments and devising new RF pulse sequence in nuclear magnetic resonance. Solid-state NMR is definitely a timely topic or area of research, and not many papers on the respective theories are available in the literature of nuclear magnetic resonance or physics reports. This report presents the power and the salient features of the promising theoretical approach called Floquet–Magnus expansion that is helpful to describe the time evolution of the spin system at all times in nuclear magnetic resonance. The report presents a broad view of algorithms of spin dynamics, based on promising and useful theory of Floquet–Magnus expansion. This theory provides procedures to control and describe the spin dynamics in solid-state NMR. Major applications of the Floquet–Magnus expansion are illustrated by simple solid-state NMR and physical applications such as in nuclear, atomic, molecular physics, and quantum mechanics, NMR, quantum field theory and high energy physics, electromagnetism, optics, general relativity, search of periodic orbits, and geometric control of mechanical systems. The aim of this report is to bring to the attention of the spin dynamics community, the bridge that exists between solid-state NMR and other related fields of physics and applied mathematics. This review article also discusses future potential theoretical directions in solid-state NMR.