Field correlation function interpretation

The persistence of the fluctuating local fields before being averaged out by molecular motion, and hence their effectiveness in causing relaxation, is described by a time-correlation function (TCF). Because the TCF embodies all the information about mechanisms and rates of motion, obtaining this function is the crucial point for a quantitative interpretation of relaxation data. As will be seen later, the spectral-density and time-correlation functions are Fourier-transform pairs, interrelating motional frequencies (spectral density, frequency domain) and motional rates (TCF, time domain). 

Here, we report some basic results that are necessary for further developments in this presentation. The merging process of a test particle is based on the concept of cavity function (first adopted to interpret the pair correlation function of a hard-sphere system [75]), and on the potential distribution theorem (PDT) used to determine the excess chemical potential of uniform and nonuniform fluids [73, 74]. The obtaining of the PDT is done with the test-particle method for nonuniform systems assuming that the presence of a test particle is equivalent to placing the fluid in an external field [36]. 

Early analyses of As in hot springs of the Taupo Volcanic Zone in New Zealand by Ritchie (1961) revealed a positive correlation between As and Cl which has since been confirmed for most geothermal fields. However, the interpretation of trends in the As/Cl ratio requires caution (Ballantyne and Moore, 1988), as the association is more a function of common behaviour, than of a common source or direct chemical association. The source of the Cl ion may be gaseous HCl associated with magma intrusion, host rock... 

After briefly reviewing conventional optical and infrared heterodyne detection, we examine the behavior of a multiphoton absorption heterodyne receiver. Expressions are obtained for the detector response, signal-to-noise ratio, and minimum detectable power for a number of cases of interest. Receiver performance is found to depend on the higher-order correlation functions of the radiation field and on the local oscillator irradiance. This technique may be useful in regions of the spectrum where high quantum efficiency detectors are not available since performance similar to that of the conventional unity quantum efficiency heterodyne receiver can theoretically be achieved. Practical problems which may make this difficult are discussed. A physical interpretation of the process in terms of the absorption of monochromatic and nonmonochromatic photons is given. The double-quantum case is treated in particular detail the results of a preliminary experiment are presented and... 

Let us first consider spectroscopy. Linear-response theory, in particular the fluctuation dissipation theorem - which relates the absorption of an incident monochromatic field to the correlation function of (e.g. dipole) fluctuations in equilibrium - has changed our perspective on spectroscopy of dense media. It has moved away from a static Schrodinger picture -phrased in terms of transitions between immutable (but usually incomputable) quantum levels - to a dynamic Heisenberg picture, in which the spectral line shape is related by Fourier transform to a correlation function that describes the decay of fluctuations. Of course, any property that cannot be computed in the Schrodinger picture, cannot be computed in the Heisenberg picture either however, correlation functions, unlike wave-functions, have a clear meaning in the classical limit. This makes it much easier to come up with simple (semi) classical interpretations and approximations. 

The discussion above has been more or less empirical and descriptive. However, considerable effort has been made to interpret 3-SCS on a more physical basis. Electric-field effects (71-75) were invoked to explain signal shifts of 3-carbon atoms induced by protonation of amines (157,158) (cf. Section II-B-3). This approach was later extended to other functionalities by Schneider and coworkers, who assumed that the SEF component (E2) rather than inductive properties of the substituents should be responsible for 3-SCS (113). They found fairly linear correlations of 3-SCS(X ) and 3-SCS(X ) in cyclohexyl derivatives (76) and attributed the difference between these for a given X to a widening of the C -Cp-Cv bond angle by 2.2° in the axial conformer (114,159). The decrease of 3-SCS in the order primary Cp —> secondary Cp — tertiary Cp — quaternary Cp was explained by electron-charge polarization in the Cp-C" bond(s) induced by the LEF component of the C -X dipole, which is already of significance at this distance, though ( 2) still dominates (160). Such an electron flow toward the 3 carbon is expected to be much more pronounced in C-C than in C-H bonds because of the polarizability difference (aCH = 0.79 acc = 1.12) (150,151,160). 

---