Advances in Theory of Solid-State Nuclear Magnetic Resonance.

Recent advances in theory of solid state nuclear magnetic resonance (NMR) such as Floquet-Magnus expansion and Fer expansion, address alternative methods for solving a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state NMR in particular. The power and the salient features of these theoretical approaches that are helpful to describe the time evolution of the spin system at all times are presented. This review article presents a broad view of manipulations of spin systems in solid-state NMR, based on milestones theories including the average Hamiltonian theory and the Floquet theory, and the approaches currently developing such as the Floquet-Magnus expansion and the Fer expansion. All these approaches provide procedures to control and describe the spin dynamics in solid-state NMR. Applications of these theoretical methods to stroboscopic and synchronized manipulations, non-synchronized experiments, multiple incommensurated frequencies, magic-angle spinning samples, are illustrated. We also reviewed the propagators of these theories and discussed their convergences. Note that the FME is an extension of the popular Magnus Expansion and Average Hamiltonian Theory. It aims is to bridge the AHT to the Floquet Theorem but in a more concise and efficient formalism. Calculations can then be performed in a finite-dimensional Hilbert space instead of an infinite dimensional space within the so-called Floquet theory. We expected that the FME will provide means for more accurate and efficient spin dynamics simulation and for devising new RF pulse sequence.