Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

Mananga, Eugene Stephane; Moghaddasi, J.; Sana, Ajaz; Sadoqi, Mostafa

doi:10.4236/wjnst.2015.51004

Cited by 5 publications

(3 citation statements)

References 92 publications

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“…In particle physics, quantum electrodynamics is the relativistic quantum field theory of electrodynamics delineating how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is concluded. The time independent Hamiltonian of FME [39][40][41][42] and FE [43] can then play a major role in the treatment of infrared divergences for some quantum electrodynamics process.…”

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confidence: 99%

Alternative Directions to Control Spin Dynamics in Nuclear Magnetic Resonance and Physics

Stephane¹

2017

Int J At Nucl Phys

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As front-line theories to control spin dynamics in solid-state nuclear magnetic resonance, the Average Hamiltonian Theory (AHT) [1] and Floquet Theory (FLT) [2,3] have assumed great prominence and influence since the development of multiple pulse sequences and the inception of Magic-Angle Spinning (MAS) methods in the 1960s [4,5]. Methods developed over the past decade have enabled us to make a significant progress in the area of NMR by introducing an alternative expansion scheme called Floquet-Magnus Expansion (FME) [6,7] used to solve the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state NMR in particular. The FME establish the connection between the Magnus Expansion (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 [6][7][8][9][10][11][12]. 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 [6]. In the same vein, Madhu and Kurur has recently introduced the Fer Expansion (FE) in Solid-State NMR [13,14]. The Fer expansion was formulated by Fer [13] and later revised by Fer [13], Klarsfeld and Oteo [15], Casas, et al. [16] and Blanes, et al. [17]. 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. A paper which outlines the comparison of both theories (FME and FE) in NMR and physics has recently been published in the Journal of Physical Chemistry A [18].

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confidence: 99%

Alternative Directions to Control Spin Dynamics in Nuclear Magnetic Resonance and Physics

Stephane¹

2017

Int J At Nucl Phys

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“…Here, we have assumed J 2 z a constant and introduced h ′ = h + β z 39 . To calculate the product of U j 's, the usual average Hamiltonian theory is not applicable because β x,y τ 10 and h ′ τ 100 beyond the 8/11 convergence radius [44][45][46][47] . We employ, instead, a continuous rotation method developed by us previously 48 , by numerically calculating the effective magnetic field β β β e .…”

Section: Rebuilding Spin Squeezing With Dynamical Decouplingmentioning

confidence: 99%

Rebuilding of destroyed spin squeezing in noisy environments

Sun

et al. 2017

Sci Rep

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We investigate the process of spin squeezing in a ferromagnetic dipolar spin-1 Bose-Einstein condensate under the driven one-axis twisting scheme, with emphasis on the detrimental effect of noisy environments (stray magnetic fields) which completely destroy the spin squeezing. By applying concatenated dynamical decoupling pulse sequences with a moderate bias magnetic field to suppress the effect of the noisy environments, we faithfully reconstruct the spin squeezing process under realistic experimental conditions. Our noise-resistant method is ready to be employed to generate the spin squeezed state in a dipolar spin-1 Bose-Einstein condensate and paves a feasible way to the Heisenberg-limit quantum metrology.

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“…A number of authors have also used the Magnus expansion and related techniques to develop numerical methods to integrate highly oscillatory differential equations [6], for example Iserles [7,8]. These Magnus-based numerical integrators have been extensively applied to problems in quantum and atomic physics [9,10], as the time dependent Schrodinger equation can be written in the form of (1.1) if we use a basis of wavefunctions [11]. Some alternative methods for solving coupled differential equations have also been explored in the context of primordial cosmology [12].…”

Section: Introductionmentioning

confidence: 99%

Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method

Bamber

Handley

2020

Phys. Rev. D

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We explore higher dimensional generalisations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve the performance and adaptability of the codes which are used compute numerical solutions to the Einstein-Boltzmann equations. We test Magnus expansion-based methods on the Einstein-Boltzmann equations for a simple universe model dominated by photons with a small amount of cold dark matter. The Magnus expansion methods achieve an increase in run speed of about 50% compared to a standard Runge-Kutta integration method. A comparison of approximate solutions derived from the Magnus expansion and the Wentzel-Kramers-Brillouin (WKB) method implies the two are distinct mathematical approaches. Simple Magnus expansion solutions show inferior long range accuracy compared to WKB. However we also demonstrate how one can improve on the standard Magnus approach to obtain a new "Jordan-Magnus" method. This has WKB-like performance on simple two-dimensional systems, although its higher dimensional generalisation remains elusive.

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Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

Cited by 5 publications

References 92 publications

Alternative Directions to Control Spin Dynamics in Nuclear Magnetic Resonance and Physics

Alternative Directions to Control Spin Dynamics in Nuclear Magnetic Resonance and Physics

Rebuilding of destroyed spin squeezing in noisy environments

Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method

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