Golden rule analysis

When Va is small so that the transition is nonadiabatic, the usual golden-rule analysis based on (5.66) can be performed to give [Garg et al. 1985 Wolynes 1987]... 

Spectral densities are positive, or at least nonnegative, functions of frequency. This follows from their physical interpretations as transition probabilities, and is clear analytically from the golden rule formula, (Eq. (3)). The positive nature of spectral densities is essential to the methods of analysis we will use in the next two sections. 

Exploration of a data set before resolution is a golden rule fully applicable to image analysis. In this context, there are two important domains of information in the data set the spectral domain and the spatial domain. Using a method for the selection of pure variables like SIMPLISMA [53], we can select the pixels with the most dissimilar spectra. As in the resolution of other types of data sets, these spectra are good initial estimates to start the constrained optimization of matrices C and ST. The spatial dimension of an image is what makes these types of measurement different from other chemical data sets, since it provides local information about the sample through pixel-to-pixel spectral variations. This local character can be exploited with chemometric tools based on local-rank analysis, like FSMW-EFA [30, 31], explained in Section 11.3. 

A similar analysis may be made for the 1D case.126 The interaction energies / (co) then show an enhancement of the order of k/a 103 relative to the parameters of the isolated point dipole, which is easily overwhelmed by nonradiative processes. Using the simple golden rule image, we may say that the transition dipole shows a huge increase from 0D to 3D systems, while the effective photon continuum density varies in an opposite (in fact complementary) way as follows, with radiative-power optimization for 2D systems ... 

The two-dimensional electron transfer diabatic free energy surfaces in Figure 7 have been analyzed with the Golden Rule rate expression given in Eq. 46. This analysis suggests that FT and EPT are possible for both systems, but FT is the dominant path due to significant overlap between the proton vibrational wave... 

Sample Size Reduction. The sample obtained from the sampler is generally larger than the sample required for analysis. If a small portion of this sample is arbitrarily scooped for analysis, it will introduce a bias. The sample size can be reduced to the analytical size using various sample reduction techniques (1) spinning riffler, (2) chute riffler, (3) ICI method, and so on. All these methods follow the golden rules for sampling. For details on these sample reduction techniques, see AUen (1981). 

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