Moment fluctuations

Neumann, M. Dipole moment fluctuation formulas in computer simvilations of polar systems. Mol. Phys. 50 (1983) 841-858. 

Changes in the occupancy of the open-channel state of the receptor as a function of time (pA2R (t)) in response to a perturbation of the receptor equilibrium can be used to obtain information about the rates of channel gating and the interaction of dmgs with ion-channel receptors. The system is said to relax towards a new equilibrium. The time course of the relaxation is used to measure rates from the average behavior of many ion channels in a recording, while noise analysis uses the frequency of the moment-to-moment fluctuations in occupancy of the open-channel state at equilibrium to provide information about the rates in the receptor mechanism. 

Questionnaires and rating scales for sleepiness can be divided into two broad categories those that estimate short-term, or moment-to-moment fluctuations, and those that assess more long-term (steady-state, permanent) states. The former is typified by the Stanford Sleepiness Scale (SSS), and is best suited for evaluation of sleepiness/alertness throughout the circadian cycle. The latter are typified by the ESS, and are best suited for the evaluation of sleep disorders. 

Ferric hydroxide, dried at 100° C., gradually becomes rehydrated upon prolonged exposure to a saturated atmosphere.2 Although the above substances are usually described as hydrates of ferric oxide, it is by no means certain that all of them are to be regarded as definite chemical entities.3 They are mostly hygroscopic substances, the amount of water they contain at any moment fluctuating with the temperature and humidity of the atmosphere. The task of determining precisely how much of the contained water is merely physically attached to the oxide, and how much is chemically combined with it, is not easy. 

This equation gives the mean-square value of the voltage appearing across the terminals of a capadtor filled with a dielectric of zero-frequency relative permittivity, s in terms of Co, the capacitance without a dielectric, and the absolute temperature, T. This noise voltage is caused by the thermally induced dipole-moment fluctuations which are themselves inextricably bound up with the dissipative processes. That this is so is indicated by the fact that equation (42) applied to aJ,to) leads to the relation... 

With local information given by INM analysis in mind, we next see the character of rotational relaxation in liquid water. The most familiar way to see this, not only for numerical simulations [76-78] but for laboratory experiments, is to measure dielectric relaxation, by means of which total or individual dipole moments can be probed [79,80]. Figure 10 gives power spectra of the total dipole moment fluctuation of liquid water, together with the case of water cluster, (H20)io8- The spectral profile for liquid water is nearly fitted to the Lorentzian, which is consistent with a direct calculation of the correlation function of rotational motions. The exponential decaying behavior of dielectric relaxation was actually verified in laboratory experiments [79,80]. On the other hand, the profile for water cluster deviates from the Lorentzian function. As stated in Section III, the dynamics of finite systems may be more difficult to be understood. 

Figure 10. The power spectrum density of the total dipole moment fluctuation of liquid water (solid line) and water cluster (H2O)108 (dashed line). The simulation of liquid water was performed for 216 water molecules under the periodic boundary condition.

Fig. 5.28 The 4/ shell of each Gd atom carries a local magnetic moment which remains constant with temperature. The relative axes of these magnetic moments fluctuate with rising temperature. This behavior can be modeled by spin waves being characterized by the angle a between nearest neighbors. From [127], copyright 1998, reproduced with permission from World Scientific Publishing Co. Pte. Ltd...

As just described, the field distribution at the muon site in a frozen, disordered (non-dilute moment) magnetic state is often not measured, because large-asymmetry muon signals are only seen at higher temperatures, where the spins are not fully frozen, and the dynamics partially decouples the muon from the large internal fields. Interpretation of the muon relaxation in terms of the behavior of the moment system generally requires a model of both the distribution of local fields caused by the moments, and the spectrum of moment fluctuations. With no detailed information on the field distribution from the static (low-temperature) limit, there can be considerable ambiguity in interpretation. 

A word of caution about fig. 132 the relaxation rate below 1 K has a completely different meaning for the single crystal relative to the polycrystalline samples. In the former, the dynamic situation prevails and the variation of relaxation rate reflects changes in the fluctuation rate of 4f moments. It rises as moment fluctuations slow down at lower temperatures. In the latter, depolarization is close to static and the rate more directly relates to the field distribution width, which increases in proportion to the rise of magnetization in an ordered magnet when temperature is reduced. 

Summary YbPdSb is magnetically unstable. The [xSR data on a sample that does not develop long-range AFM order show that the material enters a spin-liquid state instead. This state is characterized by dynamic short-range correlations whose fluctuation rate becomes temperature independent below 0.3 K at the comparatively low value of 60 MHz. Probably one deals with quantum fluctuations that are interpreted here as local moment fluctuations induced by the dynamics of fluctuating bonds of Kondo spin pairs. 

---