Statistical fine structure

Early Steps Statistical Fine Structure in Inhomogeneous Lines... 

Fig. 2.2. (A) Illustration of the source of statistical fine structure (SFS) using simulated absorption spectra with different total numbers of absorbers N, where a Gaussian random variable provides center frequencies for the inhomogeneous distribution. Traces (a) through (d) correspond to N values of 10, 100, 1,000, and 10,000, respectively, and the traces have been divided by the factors shown. For clarity, yjj = Fi/10. Inset several guest impurity molecules are sketched as rectangles with different local environments produced by strains, local electric fields, and other imperfections in the host matrix. (B) SFS detected by FM spectroscopy for pentacene in p-terphenyl at 1.4K, with a spectral hole at zero relative frequency for one of the two scans. Note the repeatable fine structure...

Figure 17. Near-field spectroscopy. Statistical fine structure and single-molecule features upon approach to the near field. Approximate distances from the surface (a) 1.2 pm, (b) 0.5 pm, and (c) 210-270 run. Each panel shows two spectra taken as 5 min apart to show reproducibility. The distance for case (c) was estimated from the background fluorescence increase (BFI) approach curve. Zero detuning = 592.066 nm,...

Fig. 17 shows three examples of fluorescence spectra measured at different distances from the surface. At 1.2 pm only statistical fine structure can be observed. In this case the illuminated area is very large and many molecules with the same resonance frequency are excited. Their fluorescence overlaps and it is not possible to distinguish individual molecules. Nevertheless, the fine structure spectrum is reproducible, as demonstrated by the two traces taken 5 min. apart. Closer to the surface the single molecule features become more pronounced. The excited volume is now smaller and... 

Figure 5. Statistical fine structure and single-molecule features upon approach to the near-field. Approximate distances from the surface (a)...

EXELFS (the extended energy-loss fine structure) carries information about the bonding and co-ordination of the atoms contributing to the edge. However, the signal needs to be strong before statistically reliable information can be obtained. 

Gibson, C. H., G. R. Stegen, and R. B. Williams (1970). Statistics of the fine structure of turbulent velocity and temperature fields measured at high Reynolds numbers. Journal of Fluid Mechanics 41, 153-167. 

The effect of averaging over one or more particle parameters—size, shape, orientation—is to efface details extinction fine structure, particularly ripple structure, to a lesser extent interference structure (Chapter 11) and undulations in scattering diagrams. If the details disappear upon averaging over an ensemble perhaps the best strategy in this instance would be to avoid the details of individual-particle scattering altogether and reformulate the problem statistically. 

It is difficult to define turbulence. Intuitively, we associate it with the fine-structure of the fluid motion, as opposed to the flow pattern of the large-scale currents. Although it is not possible to describe exactly the distribution in space and time of this small-scale motion, we can characterize it in terms of certain statistical parameters such as the variance of the current velocity at some fixed location. A similar approach has been adopted to describe the motion at the molecular level. It is not possible to describe the movement of some individual molecule, but groups of molecules obey certain characteristic laws. In this way the individual behavior of many molecules sums to yield the average motion in response to macroscopic forces. 

Fig. 4. The fine structure constant a has been determined with various methods [25-28]. most precise is the determination from the magnetic anomaly of the electron. The muonium atom offers two different routes which uses independent sets of fundamental constants. The disagreement (the error bars are mostly statistical) seem to indicate that the value h/me from neutron de Broglie wavelength measurements may be quoted with too high accuracy...

Figure 4.3-7 Rotation-vibration spectrum of C2H2 (5 hPa, 25 °C, l(i cm) at a spectral resolution of 0,05 cm with the inset the intensity alternation due to spin statistics in the /5-fundamenlal is illustrated (the underlying fine structure is from a hot band transition with its 0-branch shifted to lower wavenumbers compared to the fundamental).

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