The overall goals of this review article is to support theories in NMR in order to continue to a) apply the av- erage Hamiltonian theory to problems including (but not limited to): a class of symmetrical radio-frequency pulse sequences in the NMR of rotating solids, the symmetry principles in the design of NMR multiple-pulse sequences, the composite pulses, and the problems still unsolved such as the AHT for 3 spins -; b) use the Floquet theory in the study of several magic-angle spinning (MAS) NMR experiments on spin systems with a periodically time-dependent Hamiltonian such as the multiple-multimode Floquet-theory in NMR ; c) en- hance the performance of the Floquet-Magnus expansion by considering fundamental questions that arise when dealing with this approach . Using FME method, many interesting problems will be approached such as multi-mode Hamiltonian, rotational-resonance recoupling, continuous wave irradiation on a single species, DARR and MIRROR recoupling, C-type and R-type sequences, TPPM decoupling, etc.   ; d) use the Fer expansion to solve similar problems such as those solved using the AHT ; e) explore potential future theoretical and numerical directions for the calculation of the time propagation and evolution operators using Chebychev expansion and Cayley transformation methods  -. It is noteworthy that unifying or com- bining two and more theories known in NMR will continue to provide a framework for treating time-dependent Hamiltonian in quantum physics and NMR in a more efficient way that can be easily extended to all types of modulations.
A question that is central to understanding the dynamics of entangled polymer molecules concerns whether linear chains in semi-dilute solution reptate . P GSE, along with neutron scattering, is one of the few techniques able to adequately probe the internal motions of polymers in this state, due to the ability to measure the self-motion of molecules as opposed to relative motion. The dynamic distances appropriate for polymer diffusion measurements are of the order of 50 to 5000 A. Unfortunately neutron scattering i s confined to measuring displacements of less than 50 A while, until recently, PGSE NMR has been confined to measurements above 1 000 A displacement. Recent improvements[25, 54] to the PGSE NMR method have reduced this lower limit by an order of magnitude. One such method, the PGSE MASSEY technique , is used to obtain some of the results presented here. The time window available is determined by the available gradient amplitude and by spin relaxation. In the present instance it is from 10 ms to 1 s .
2.2 of chapter 6 presents simulations of longitudinal relaxation for this regime. Note that if the spin system were temporarily moved out of the large applied field, the nonsecular part of the dipolar Hamiltonian would be "turned on," and we could expect a spin temperature to be established, so that the system could be viewed as an ensemble of independent spins. If the secular dipolar Hamiltonian is found to couple angular momentum systems too weakly for eﬃcient cooling, moving the spin-resonator system adiabatically in and out of the high field might speed up the relaxation. When the spins have been moved out of the high field, a low spin temperature would correspond to a strong dipole order. Moving the system adiabatically back into the high field would convert the dipolar order of the thermal spin system to Zeeman order, and interactions with the resonator could then cool the system for a period of time until the ground states of the angular momentum systems have accumulated excess population and the cooling has slowed. The changes in the field at the spins would need to be slow enough that the entropy of the spin system would not change as the
a a c c , which describe multiple-magnon scattering and do not contribute to a net change in magnetization along the spin-quantization axis have disregarded. It also is disregarded higher-order terms associated with the Holstein-Primakoff expansion. Fully addressing magnonic correlation effects in the ultrafast regime would require a rigorous approach, e.g., using nonequilibrium Keldysh formalism . However, when the s-d coupling (20) is not the dominant contribution to H , a mean-field approach and Fermi’s golden rule were used to compute the spin transfer between the s and d subsystems. Additionally, it is assumed that all relevant energy scales are much smaller than the Fermi energy ε = k T B F of the itinerant
inhomogeneous electron spin dephasing occurring over a few nanoseconds as a consequence of precession in the slowly changing nuclear Overhauser field is well understood and measured [19–21]. Surprisingly, first experimental data on the time scales of the nuclearspin bath dynamics in QDs have only recently emerged, reporting in one case correlation times of 100 μs (5.5 μs) for a resonantly driven negatively charged (neutral) QD  and in the other case nuclear coherence times of a few milliseconds for a neutral QD . The dynamics, assigned to nuclear dipolar coupling in both reports, were obtained in the absence of an external magnetic field in the former and at fields of a few Tesla in the latter case. Studying nuclearspin bath dynamics for a driven QD is complicated by the simultaneously occurring electric field fluctuations which mask the optical signatures of the nuclear bath evolution. Recently, the advantage of resonant excitation for sensitive measurements was demonstrated by Kuhlmann et al., who identified two features in the power spectrum of QD resonance fluorescence attributed to electric and magnetic field noise . However, a reliable method to isolate the effects of nuclearspin fluctuations, which would allow a direct study of their dynamics, is still missing.
NuclearMagneticResonance (NMR) spectroscopy is an analytical chemistry technique used in quality control and research for determining the content and purity of a sample as well as its molecular structure. NMR is also the most powerful technique used to obtain structural information, and therefore it can help to understand the structure of components in food complex systems 1,2 . 1 H NMR and 13 C NMR spectroscopies are used for analyses of all
o then for each of the spins there are H+l levels with energy spacing • The nucleus at resonance in the Investigations reported here is the proton, which has spin Hence the energy separation of the two possible states Is 2^ n„ i these correspond to^ parallel or anti parallel to the field H . Transitions between the two states are allowed and hence energy absorption can occur* For this to happen quanta of energy, , must be supplied from an electromagnetic field, viz
For a large enough sample θ will run all the way from 0 to 2π. ∗ Sadly, the limits for φ are not so simply determined. Since samples are mostly flat, and because the resonant slices are not spherical , the range of φ will depend on θ (Illustrated in figure 2.2). But as soon as we have solved this problem, finite depth samples are no challenge any more, since for a sample of depth D the signal will be the difference between an infinite sample at height d and one at height d + D. The equation relating the height above the sample d and the edge of the resonance slice at angles φ and θ is the following:
To conclude, our atomistic spin modeling and phe- nomenological theory, supported by element-speci¯c fs XMCD experiments, demonstrate the possibility of tuning the dynamics of multi-sublattice ferro- magnets and ferrimagnets by their composition, which determines their magnetic moments and the strength of the exchange interaction. This can lead to distinctly di®erent demagnetization times even for the same element in di®erent alloys. In particu- lar, we have shown that for antiferromagnetic coupling, exchange relaxation accelerates the de- magnetization of both sublattices, while with ferro- magnetic coupling, the dynamics of one sublattice is accelerated while the other is slowed down. Fur- thermore, we have shown that, by tuning the com- position we can control the distinctiveness of the
This bibliography lists the titles of literature articles in the field of nuclear quadrupole resonance spectroscopy of solids. This field has been taken to include the area of quadrupolar effects in nuclearmagneticresonance as well as 3 the basic area of nuclear quadrupole resonance in zero magnetic field. Articles published not later than January 1, 1958 have been included. Twenty-one journals are represented, and in addition, eleven books which contain chapters or sections dealing with this subject are included.
CONCLUSIONS. Deep gray matter spin-spin relaxation time was increased in the first few days after birth in infants with an adverse outcome. Proton magneticresonance spectroscopy was more prognostic than spin-spin relaxation time, with lactate/N- acetylaspartate the best measure. Nevertheless, both techniques were useful for early prognosis, and the potential superior spatial resolution of spin-spin relaxometry may define better the precise anatomic pattern of injury in the early days after birth.
Aggrecan, a highly charged macromolecule found in articular cartilage, was investigated in aqueous salt solutions with proton nuclearmagneticresonance. The longitudinal and transverse relaxation rates were determined at two different field strengths, 9.4 T and 0.5 T, for a range of temperatures and aggrecan concentrations. The diffusion coefficients of the water molecules were also measured as a function of temperature and aggrecan concentration, using a pulsed field gradient technique at 9.4 T. Assuming an Arrhenius relationship, the activation energies for the various relaxation processes and the translational motion of the water molecules were determined from temperature dependencies as a function of aggrecan concentration in the range 0–5.3% w/w. The longitudinal relaxation rate and inverse diffusion coefficient were approximately equally dependent on concentration and only increased by upto 20% from that of the salt solution. The transverse relaxation rate at high field demonstrated greatest concentration dependence, changing by an order of magnitude across the concentration range examined. We attribute this primarily to chemical exchange. Activation energies appeared to be approximately independent of aggrecan concentration, except for that of the low-field transverse relaxation rate, which decreased with concentration.
Brief history Felix Bloch (1) at Stanford University and Edward Purcell and his colleagues (2) at Harvard University reported the phenomenon of NMR independently in 1946. As a result, Bloch and Purcell shared the 1952 Nobel Prize in Physics. Between 1950 and 1970, NMR spectroscopy was developed and used to analyze chemical and physical molecular structure. In 1971, Raymond Damadian reported that the NMR relaxation times of tumors differed from those of normal tissue, suggesting for the first time that magneticresonance (MR) might be used for the detection of disease (3). In 1973, Paul Lauterbur was the first to report that images could be generated by NMR using small test tube samples of water and oil (4). Rather than creating a homogeneous magnet field by adjusting the “shimming” magnets to minimize field inhomogeneity, Lauterbur applied a magnetic field gradient to induce inhomogeneity in a planned way, providing a method to encode different parts of the substance to be imaged. He generated images using a technique analogous to that