On the equivalence of different effective hamiltonians which determine the dynamics of a spin system in rapidly oscillating periodic fields

Quantum-mechanical evolution of systems with periodic time-modulated Hamiltonians is often described by effective interactions. Such average Hamiltonians, calculated as few terms of an expansion in powers of the interaction, are sometimes difficult to relate to experimental observations. We propose a frequency-domain approach to this problem, which offers certain advantages and produces an approximate solution for the density matrix, better linked to measurable quantities. The formalism is suitable for calculating the intensities of narrowed spectral peaks. Fast magic-angle-spinning NMR spectra of solids are used to experimentally illustrate the method.

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“…It can be also obtained by using the Liouvillian in Eq. (10) in the expansion in Eq. (4b) as following.…”

Section: Theorymentioning

confidence: 99%

“…Equivalence of different effective Hamiltonians has been discussed in Ref. 10. The average Liouvillian theory [11][12][13] can be developed in a similar way.…”

Section: Introductionmentioning

confidence: 99%

Coherent averaging in the frequency domain

Khitrin

Ramamoorthy

2012

The Journal of Chemical Physics

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“…Methods developed over the past decade have enabled us to make a significant progress in the area of solid-state NMR by introducing an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state NMR in particular [9] [11] [24]. The FME establish the connection between the ME and the Floquet theory, and provides a new version of the ME well suited for the Floquet theory for linear ordinary differential equations with periodic coefficients [9] [11] [24] [25] [26] [27]. We have proved that the ME is a particular case of the FME which yields new aspects not present in ME and Floquet theory such as recursive expansion scheme in Hilbert space that can facilitate the implementation of new or improvement of existing pulse sequences [24] [28].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Perspectives of Spin Dynamics in Solid-State Nuclear Magnetic Resonance and Physics

Mananga¹

2018

JMP

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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.

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“…In the average Hamiltonian theory (AHT) [2], for instance, the E H (or the average Hamiltonian) depends on the initial point of the time interval (to, to + to) used for the EH calculation. I n order to eliminate this ambiguity one has to perform a proper transformation of the initial density matrix [3]. Another and more important reason lies in the fact that the expansion of the E H is divergent due to the multispin resonance processes [4].…”

Section: Introductionmentioning

confidence: 99%