Multipole operators for an arbitrary number of spins

Sanctuary, B. C.

doi:10.1063/1.432104

Cited by 113 publications

(54 citation statements)

References 8 publications

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“…In this situation, the raising and lowering operators give particularly simple equations of motion, given in Eq. [11].…”

Section: Manipulating the Density Matrixmentioning

confidence: 95%

Operator formalisms: An overview

Bain

2006

Concepts Magnetic Resonance

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ABSTRACT:Operator formalisms are mathematical recipes for simplifying the manipulations of the density matrix. Because the density matrix is a vital tool in describing and analyzing magnetic resonance experiments, many approaches have been developed. This article gives an overview of a number of different methods: spherical tensors, fictitious spin-1/2, single-transition operators, product operators, superspin methods, and others. In principle, they all must give the same answer, because an exact description of magnetic resonance phenomena is usually within reach. The choice of the formalism for the user, therefore, depends on various personal decisions. Among these decisions is the choice between spherical and Cartesian tensors, between Hilbert space and Liouville space, between commutators and matrix elements, and so on. We do not go into the details of any of the formalisms but rather try to compare their approaches at a fairly general level. The quadrupolar echo pulse sequence is used as an example of the application of the formalisms. The aim of this overview is to give readers enough of a picture so that they can make an intelligent choice for themselves.

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“…In this situation, the raising and lowering operators give particularly simple equations of motion, given in Eq. [11].…”

Section: Manipulating the Density Matrixmentioning

confidence: 95%

Operator formalisms: An overview

Bain

2006

Concepts Magnetic Resonance

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“…This formalism is the most useful in the case of two coupled angular momenta due to the difficulty of coupling multiple angular momenta, but attempts at the general case have been made [505]. Only the case of two angular momenta will be considered here.…”

Section: Calculation Of the Distant Dipolar Field For Cylindricallymentioning

confidence: 99%

Nuclear magnetic resonance studies of quadrupolar nuclei and dipolar field effects

Urban

2004

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Experimental and theoretical research conducted in two areas in the field of nuclear magnetic resonance (NMR) spectroscopy is presented: (1) studies of the coherent quantummechanical control of the angular momentum dynamics of quadrupolar (spin I > 1/2) nuclei and its application to the determination of molecular structure; and (2) applications of the long-range nuclear dipolar field to novel NMR detection methodologies.The dissertation is organized into six chapters. The first two chapters and associated appendices are intended to be pedagogical and include an introduction to the quantum mechanical theory of pulsed NMR spectroscopy and the time dependent theory of quantum mechanics.The third chapter describes investigations of the solid-state multiple-quantum magic angle spinning (MQMAS) NMR experiment applied to I = 5/2 quadrupolar nu-2 clei. This work reports the use of rotary resonance-matched radiofrequency irradiation for sensitivity enhancement of the I = 5/2 MQMAS experiment. These experiments exhibited certain selective line narrowing effects which were investigated theoretically.The fourth chapter extends the discussion of multiple quantum spectroscopy of quadrupolar nuclei to a mostly theoretical study of the feasibility of enhancing the resolution of nitrogen-14 NMR of large biomolecules in solution via double-quantum spectroscopy.The fifth chapter continues to extend the principles of multiple quantum NMR spectroscopy of quadrupolar nuclei to make analogies between experiments in NMR/nuclear quadrupolar resonance (NQR) and experiments in atomic/molecular optics (AMO). These analogies are made through the Hamiltonian and density operator formalism of angular momentum dynamics in the presence of electric and magnetic fields.The sixth chapter investigates the use of the macroscopic nuclear dipolar field to encode the NMR spectrum of an analyte nucleus indirectly in the magnetization of a sensor nucleus. This technique could potentially serve as an encoding module for the recently developed NMR remote detection experiment. The feasibility of using hyperpolarized xenon-129 gas as a sensor is discussed. This work also reports the use of an optical atomic magnetometer to detect the nuclear magnetization of Xe-129 gas, which has potential applicability as a detection module for NMR remote detection experiments.

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“…The multipole-multimode Floquet theory (MMFT) presented by Ramachandran and Griffin in its first application still remains a viable alternative for describing both coherent as well as incoherent effects observed in NMR experiments [83]. On one hand, Ramachandran and Griffin combined Shirley's Floquet approach to the multipole theory proposed by Sanctuary in order toexpand any periodic time-dependent spin Hamiltonian, density operator, and Liouville superoperator in a Fourier series [83]- [85]. Substituting the Fourier expansions of the density operator and the Liouville super-operator in the Liouville equation, the following new set of coupled differential equations spanning an infinite dimensional vector space, with time-independent coefficients were obtained…”

Section: Floquet Theorymentioning

confidence: 99%

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

Mananga¹,

Moghaddasi²,

Sana³

et al. 2015

WJNST

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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.

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Multipole operators for an arbitrary number of spins

Cited by 113 publications

References 8 publications

Operator formalisms: An overview

Operator formalisms: An overview

Nuclear magnetic resonance studies of quadrupolar nuclei and dipolar field effects

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

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