Magnetic fields fluctuating

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

Large temperature variation between streams will lead to magnetic field fluctuations that will reduce the repeatability of the NMR experiment. 

The magnetic field fluctuation is approximately 5.6 x 104 T over a range of about 10 15 m, and lasts for about 10 23 s. Fluctuations on this scale occur at about the classical radius of the electron. 

In terms of the variable of integration p, 1 < p < oo, without the magnetic-field fluctuations that necessarily go with ionic currents from the displacement of ionic charge, the n = 0 term in the van der Waals interaction between the two suspensions across m is [see Eqs. (L3.192)-(L3.194)]... 

We look at the electric- and magnetic-field fluctuations in terms of Fourier components El0 and Hl0 such that, as functions of time, these fields are... 

In addition to the electrical fluctuations, there are all the magnetic-field fluctuations that satisfy the same kind of condition. By inspection, we can see that these magnetic modes are to be determined in exactly the same way as the electrical modes, but we use the magnetic susceptibilities //m, pL, and pR, rather than sm, eL, and eR ... 

The power spectrum of the local magnetic field fluctuations shows different features at different Larmor frequency and temperature. The interpretation of the results is that the dominant source of these fluctuations is spatial transport of the electrons along the polymer chains and the frequency and temperature dependences reflect the details of their motions. 

FIGURE 3.3 Effect of molecular weight on the spectral density function. The spectral density function, J(C0), is plotted vs. the frequency of the magnetic field fluctuations. The spectral density functions for a large protein (25 kDa) and a small protein (2.5 kDa) are shown. The frequency for single quantum transition of the H spins is indicated by the arrow. 

The fundamental requirement for longitudinal relaxation of a spin- /a nucleus is a time-dependent magnetic field fluctuating at the Larmor frequency of the nuclear spin. Only through this can a change of spin state be induced or, in other words, can relaxation occur. Local magnetic fields arise from a... 

Longitudinal spin relaxation requires a stimulus in the form of a magnetic field fluctuating at a frequency equal to the frequency (energy) of the transition. In the case of dipolar relaxation, this arises from the time-dependent field a spin experiences from its dipolar coupled neighbour as the molecule rotates or tumbles in solution. The NOE in turn is dependent upon the rates of molecular tumbling. 

If qubits are stored in hyperfine sublevels of the ground rovibrational electronic state the phase is relatively insensitive to local fluctuations of dc and ac electric fields, but more sensitive to magnetic field fluctuations, which should be minimized. The time scale of this minimization should be of the order of the coherence time of the trap. The states used to switch on the dipole-dipole interaction have to be long-lived to minimize decoherence from spontaneous emission. With gate operation times of <100 (jLsec and metastable excited state lifetimes of several hundred millisecond, decoherence due to spontaneous emission will be small. 

The exponential dependence on inverse temperature, predicted by eqs. (186) and (187), is characteristic of the spin-lattice relaxation of nuclei of lanthanide ions in the VV paramagnets in a certain temperature region. Some experimental results on nuclear relaxation, induced by hyperfine magnetic field fluctuations, are given in table 15. 

The rate of relaxation is affected by magnetic field fluctuations in the local environment of excited hydrogen spins. For simple liquids such as water, the diffusion of H2O molecules by Brownian motion allows H spins to encounter and interact with other dipole magnetic moments as described by the Bloembergen-Purcell-Pound, or BPP, theory (Bloembergen et al. 1948). In cementitious materials, there are two main sources of relaxation ... 

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