Many-body processes

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Figure 3.1 Appetite is controlled by many body processes, as shown here. The arrows indicate things that increase and decrease hunger. All of these processes work by sending signals to the brain to indicate a feeling of hunger or satiety (fullness). Certain diet pills called appetite suppressants may work in the same way as some of these body processes, by sending signals to the brain that indicate satiety and say stop eating ...

Translational spectra involving molecules show similar dips, see as an example the upper part of Fig. 3.5 which was recorded with hydrogen at room temperature. A more refined treatment of the intercollisional process must take into account not only two arbitrarily selected consecutive collisions. Rather, correlations to all orders are important which render the intercollisional interference a many-body process, not exactly the three-body mechanism our simplified discussion above seems to suggest. 

Measurements. Evidence for many-body processes beyond the intercolli-sional dip is presented in Fig. 3.6 which shows the variation of the moment yi = f a(v)dv with the product of the densities [329], gig2- For strictly binary interactions, a straight line is expected and is indeed observed at the lower values of the product of densities. Above a certain threshold that is different for each system shown, superlinear dependences are observed that indicate the emergence of spectral components arising from higher than binary interactions. 

Later studies showed the same phenomena in deuterium and deuterium-rare gas mixtures [335, 338, 305], and also in nitrogen and nitrogen-helium mixtures [336] in nitrogen-argon mixtures the feature is, however, not well developed. The intercollisional dip (as the feature is now commonly called) in the rototranslational spectra was identified many years later see Fig. 3.5 and related discussions. The phenomenon was explained by van Kranendonk [404] as a many-body process, in terms of the correlations of induced dipoles in consecutive collisions. In other words, at low densities, the dipole autocorrelation function has a significant negative tail of a characteristic decay time equal to the mean time between collisions see the theoretical developments in Chapter 5 for details. 

Relationship with the intercollisional dip. The cancellation effect described by the doubly primed spectral moments y(naab>", y, abb ", is of course related to the intercollisional interference process observed near zero frequency, Fig. 3.5. The important difference is that the spectral moments are ternary quantities by design while the intercollisional dip is affected by many-body processes. 

Intercollisional interference is a many-body process. Poll (1980) has pointed out that, no matter how low the gas densities actually are, this many-body effect will always have to be reckoned with, for principal reasons. In more practical terms, at low densities intercollisional dips are generally reasonably well separable from the intracollisional profiles, because intercollisional profiles are relatively sharp while intracollisional ones are rather diffuse. In other words, a reasonably clear distinction between binary and many-body profiles is straightforward in low-density recordings. For this reason, separate theoretical discussions of the intra-and intercollisional processes are convenient and quite natural. 

The theory of line shapes of systems involving one or more molecules starts from the same relationships mentioned in Chapter 5. We will not repeat here the basic developments, e.g., the virial expansion, and proceed directly to the discussion of binary molecular systems. It has been amply demonstrated that at not too high gas densities the intensities of most parts of the induced absorption spectra vary as density squared, which suggests a binary origin. However, in certain narrow frequency bands, especially in the Q branches, this intensity variation with density q differs from the q2 behavior (intercollisional effect) the binary line shape theory does not describe the observed spectra where many-body processes are significant. In the absence of a workable theory that covers all frequencies at once, even in the low-density limit one has to treat the intercollisional parts of the spectra separately and remember that the binary theory fails at certain narrow frequency bands [318],... 

As the density of a gas is increased and/or its temperature is lowered towards or below the critical temperature, Tc, new phenomena associated with the trapping and localization of positrons are sometimes encountered, indicating that many-body processes affect positron annihilation. We briefly describe these phenomena here, but a much more detailed treatment can be found in the review of Iakubov and Khrapak (1982). 

Q10 Many body processes, including thyroid function, are controlled by negative feedback mechanisms. Explain what is meant by the term negative feedback. 

Although cholesterol has a bad reputation, it serves many important ftmctions in the body. Like phospholipids and giycolipids, cholesterol is part of cell membranes. Cholesterol also serves as a starting material (or precursor) for the body to synthesize other steroids such as testosterone, a principal male hormone, and estrogen, a principal female hormone. Hormones are chemical messengers that regulate many body processes, such as growth and metabolism. They are secreted by specialized tissues and transported in the blood. 

Small particles are also observed to melt in computer simulations at temperatures well below bulk melting. Rare gas clusters as small as 13 particles show apparent phase transitions, although of course at small sizes these are rounded rather than sharp transitions and resemble conformational equilibria more than collective many-body processes. A simulation of gold particles revealed a three-step process for the melting of the larger particles onset of surface diffusion, formation of liquid patches at the surface, and abrupt melting of the whole cluster. The 477-atom cluster melted at 800 K and the 219-atom cluster below 600 K. 

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