This paper investigates the concept of Cross Polarization (CP) experiment in addition to revisiting the two potential expansion schemes recently developed in the field of solid-state nuclear magnetic resonance (SSNMR)...This paper investigates the concept of Cross Polarization (CP) experiment in addition to revisiting the two potential expansion schemes recently developed in the field of solid-state nuclear magnetic resonance (SSNMR): namely, the Floquet-Magnus expansion and the Fer expansion. We use the aforementioned expansion schemes for the calculation of effective Hamiltonians and propagators when the spin system undergoes Cross Polarization radiation. CP is the gateway experiment into SSNMR. An in-depth comprehension of the underlying mechanics of spin dynamics during the cross-polarization experiment is pivotal for further experimental developments and optimization of more complex solid-state NMR experiments. The main contribution of this work is a prospect related to spin physics;particularly regarding to generalization of the calculation. This work reports original yet interesting novel ideas and developments that include calculations performed on the CP experiment. In fact, the approach presented could play a major role in the interpretation of several fine NMR experiments in solids, which would in turn provide significant new insights in spin physics. The generality of the work points towards potential applications in problems related in solid-state NMR and theoretical developments of spectroscopy as well as interdisciplinary research areas as long as they include spin dynamics concepts.展开更多
Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today...Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today. Much progress has been made in the utilization of solid-state NMR to illuminate molecular structure and dynamics in systems not controllable by any other way. NMR deals with time-dependent perturbations of nuclear spin systems and solving the time-dependent Schrodinger equation is a central problem in quantum physics in general and solid-state NMR in particular. This theoretical perspective outlines the methods used to treat theoretical problems in solid-state NMR as well as the recent theoretical development of spin dynamics in NMR and physics. The purpose of this review is to unravel the versatility of theories in solid-state NMR and to present the recent theoretical developments of spin dynamics.展开更多
The subject matter of this paper is the representation of the solution of the linear differential equation Y = AY - YB, Y(0) = Yo, in the form y(t) = eΩ(t)Y0 and the representation of the function n as a generalizati...The subject matter of this paper is the representation of the solution of the linear differential equation Y = AY - YB, Y(0) = Yo, in the form y(t) = eΩ(t)Y0 and the representation of the function n as a generalization of the classical Magnus expansion. An immediate application is a new recursive algorithm for the deriVation of the Baker- Campbell-Hausdorff formula and its symmetric generalization.展开更多
The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operato...The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operator.In a sense,such semi-discretization is equivalent to the Hagedorn wavepacket method,but this discretization is more intuitive to show the advantages of wavepacket methods.Moreover,we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation.The improved algorithms are of the Gauss–Hermite spec-tral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation.And for the given accuracy,the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation.The superiority is shown by the error estimation and numerical experiments.展开更多
文摘This paper investigates the concept of Cross Polarization (CP) experiment in addition to revisiting the two potential expansion schemes recently developed in the field of solid-state nuclear magnetic resonance (SSNMR): namely, the Floquet-Magnus expansion and the Fer expansion. We use the aforementioned expansion schemes for the calculation of effective Hamiltonians and propagators when the spin system undergoes Cross Polarization radiation. CP is the gateway experiment into SSNMR. An in-depth comprehension of the underlying mechanics of spin dynamics during the cross-polarization experiment is pivotal for further experimental developments and optimization of more complex solid-state NMR experiments. The main contribution of this work is a prospect related to spin physics;particularly regarding to generalization of the calculation. This work reports original yet interesting novel ideas and developments that include calculations performed on the CP experiment. In fact, the approach presented could play a major role in the interpretation of several fine NMR experiments in solids, which would in turn provide significant new insights in spin physics. The generality of the work points towards potential applications in problems related in solid-state NMR and theoretical developments of spectroscopy as well as interdisciplinary research areas as long as they include spin dynamics concepts.
文摘Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today. Much progress has been made in the utilization of solid-state NMR to illuminate molecular structure and dynamics in systems not controllable by any other way. NMR deals with time-dependent perturbations of nuclear spin systems and solving the time-dependent Schrodinger equation is a central problem in quantum physics in general and solid-state NMR in particular. This theoretical perspective outlines the methods used to treat theoretical problems in solid-state NMR as well as the recent theoretical development of spin dynamics in NMR and physics. The purpose of this review is to unravel the versatility of theories in solid-state NMR and to present the recent theoretical developments of spin dynamics.
文摘The subject matter of this paper is the representation of the solution of the linear differential equation Y = AY - YB, Y(0) = Yo, in the form y(t) = eΩ(t)Y0 and the representation of the function n as a generalization of the classical Magnus expansion. An immediate application is a new recursive algorithm for the deriVation of the Baker- Campbell-Hausdorff formula and its symmetric generalization.
基金supported by projects NSF of China(11271311)Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)Hunan Province Innovation Foundation for Postgraduate(CX2011B245).
文摘The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operator.In a sense,such semi-discretization is equivalent to the Hagedorn wavepacket method,but this discretization is more intuitive to show the advantages of wavepacket methods.Moreover,we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation.The improved algorithms are of the Gauss–Hermite spec-tral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation.And for the given accuracy,the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation.The superiority is shown by the error estimation and numerical experiments.
