Generalized susceptibility models

As for the previous example described in Sect. 3.2.1, the relaxation of the magnetization has been studied using combined ac (Fig. 6a) and dc (Fig. 6b) measurements. In order to extract the relaxation time of the system (r), the obtained frequency dependence of the in-phase x and out-of-phase x" susceptibilities and furthermore the Cole-Cole plots (x" vs. x plot) were fitted simultaneously to a generalized Debye model (solid lines in Figs. 6a and 6b). The fact that the found a parameters of this model are less than 0.06, indicates that the system is close to a pure Debye model with hence a single relaxation time. This indication is confirmed by the quasi-exponential decay of the magnetization observed between 1.8 and 0.8 K (Fig. 6b). 

Real Fermi surfaces are never perfectly planar. But the one-dimensional model is far less restrictive than it may appear to be. For example, if two sheets of Fermi surface of arbitrary shape may be brought into point-by-point coincidence by a translation vector Q, the generalized susceptibility function will have the logarithmic singularity at Q. Such two sheets of Fermi surface are said to nest , and the vector Q need not be oriented normal to the sheets. In practice even this less restrictive form of nesting is not realized because the... 

Fig. 3.65. The generalized susceptibility functions of one-, two-, and three-dimensional free electron models (Kasuya, 1%6).

Fig. 3.67. The generalized susceptibility functions for the perfect nesting model and the imperfect nesting model.

Fig. 3.73. The effect of magnetic ordering on the generalized susceptibility function of the nearly free electron -model (Elliott and Wedgwood, 1964).

An important characteristic of the optical constants is that they fall in a broad class of generalized susceptibilities with the fundamental property that their real and imaginary parts are connected by Kramers-Kronig (KK) integral relations (Landau and Lifshitz 1992). For the case of linear response, KK relations are model independent since they rely only on the causality principle and analytical properties of the complex susceptibilities. The physical reasoning behind the KK relations is that dissipation of energy of the... 

It does suggest, however, that our original assumptions concerning d were at least reasonable. In addition, the dose-depen-dent model can be manipulated to examine - in a general sense -some aspects of interspecies variations in susceptibility to nitrosamine carcinogenesis. 

In solution, although solute contributions can generally be singled out, difficulties arise sometimes solvent-solute interactions may induce a shift of the solute absorption and consequently of its susceptibility or hydrogen bonded molecular complexes may modify the liquid structure. This situation has been studied both theoretically and experimentally by Zyss and Berthier (10) and by Ledoux and Zyss (13) in the case of urea derivatives in various solvents and in crystal showing the importance of environment considerations and thus the limitations of an oriented gas model for crystals. 

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