On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

Mananga, Eugene Stephane

doi:10.1016/j.physrep.2015.10.006

Cited by 17 publications

(25 citation statements)

References 249 publications

(326 reference statements)

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“…As discussed in the next section, the convergence of Fer expansion is much faster than that of Magnus expansion, which lead to the calculation of the infinite number of commutators to be simple in most expereiments [30]. Indeed, from the point of view of physical applications, the Magnus expansion has been extensively used in a variety of issues, while the Fer expansion has been either ignored or misquoted until recently [35].…”

Section: In the Beginningmentioning

confidence: 99%

“…The appropriateness of the FME and FE are well related to the problem of convergence. This problem has played a pivotal role in the field of solid-state NMR and spin dynamics [8] [12] [25] [35]. FME and FE are divergent approaches and the physical nature of their divergences is discussed in the following paragraphs.…”

Section: Convergencementioning

confidence: 99%

“…This expansion employs the form of a product of sub-propagators, which appears to be suitable for examination of time-dependence of the density matrix for each average Hamiltonian at different orders. Some papers which outline the comparison of both theories (FME and FE) in NMR and physics were recently published in the solid-state NMR, chemical physics, and physics [34] [35].…”

Section: Introductionmentioning

confidence: 99%

“…The authors gave a rigorous relationship between the FME and general properties of transient quantum dynamics. New avenues of exploring FME and FE can also be extended to other areas of physics such as particles and high energy physics[25] [35]. These two approaches (FME and FE) can be used to solve problems in quantum field theory (QFT) and high energy physics, in particular problems similar to the one solved or fail to be solved by ME.…”

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confidence: 99%

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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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Section: In the Beginningmentioning

confidence: 99%

Section: Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Mananga¹

2018

JMP

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“…The Fer expansion was formulated by Fer in 1958 and later revised by Fer, Klarsfeld and Oteo, Casas, Blanes and coworkers 32,33 . The FE approach was recently introduced to the NMR community by Madhu and Kurur in 2006 via the effect of Bloch-Siegert shift and heteronuclear dipolar decoupling 34,35 . While the Magnus expansion and Floquet theory are common in solid-state NMR field, the Fer method is a relatively new comer although the mathematical formalism has been known for several decades.…”

Section: Significancementioning

confidence: 99%

Efficient numerical integrator based on Fer expansion: Application to solid-state NMR experiments and to solve quantum Liouville equation and quantum Fokker-Planck equation

Mananga

2017

JAP

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There are two important related research areas that I propose to investigate. First, we plan to develop an efficient numerical integrator based on Fer expansion for solid-state NMR simulation of experiments. Second, we intend to extend the method to solve quantum Liouville equation and quantum Fokker-Planck equation in order to improve the understanding of the dynamics of quantum systems subject to dissipation due to its relation to macroscopic quantum phenomena. The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance in general and solid-state NMR (SSNMR) in particular. The Fer integrator will provide to experts in quantum mechanics, NMR spectroscopy, and spin dynamics researchers, additional means for controlling spin dynamics in SSNMR. The efficient diagram will be used to compare the different orders of the Fer integrators obtained.

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Application of Floquet-Magnus and Fer expansion approaches during spin-locking radiation in solid-state NMR

Mananga

2019

Chemical Physics Letters

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On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

Cited by 17 publications

References 249 publications

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

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

Efficient numerical integrator based on Fer expansion: Application to solid-state NMR experiments and to solve quantum Liouville equation and quantum Fokker-Planck equation

Application of Floquet-Magnus and Fer expansion approaches during spin-locking radiation in solid-state NMR

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