This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories...This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method.展开更多
In this paper, a hybrid algorithm for accelerating the double series of Floquet vector modes arising in the analysis of frequency selective surfaces （FSS） is presented. The asymptotic terms with slow convergence in ...In this paper, a hybrid algorithm for accelerating the double series of Floquet vector modes arising in the analysis of frequency selective surfaces （FSS） is presented. The asymptotic terms with slow convergence in the double series are first accelerated by Poisson transformation and Ewald method, and then the remained series is accelerated by Shank transformation. It results in significant savings in memory and computing time. Numerical examples verify the validity of the hybrid acceleration algorithm.展开更多
文摘This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method.
基金supported in part by the National High-Tech Research Plan of China(863 Plan)(Grant Nos.2002AA123031 and 2003AA123310)in part by the National Natural Science Foundation of China(Grant No.60471016).
文摘In this paper, a hybrid algorithm for accelerating the double series of Floquet vector modes arising in the analysis of frequency selective surfaces （FSS） is presented. The asymptotic terms with slow convergence in the double series are first accelerated by Poisson transformation and Ewald method, and then the remained series is accelerated by Shank transformation. It results in significant savings in memory and computing time. Numerical examples verify the validity of the hybrid acceleration algorithm.
