Perturbation theory inhomogeneous systems

In the framework of many-body perturbation theory, we have studied the nonlinear interaction of charged particles with a free gas of interacting electrons. We have presented general procedures to calculate the nonlinear potential induced by charged particles moving in an inhomogeneous electron system, the Zj contribution to the stopping power of a FEG, and double-plasmon excitation probabilities. 

The development and application of generalized perturbation theory (GPT) has made considerable progress since its introduction by Usachev (i(S). Usachev developed GPT for a ratio of linear flux functionals in critical systems. Gandini 39) extended GPT to the ratio of linear adjoint functionals and of bilinear functionals in critical systems. Recently, Stacey (40) further extended GPT to ratios of linear flux functionals, linear adjoint functionals, and bilinear functional in source-driven systems. A comprehensive review of GPT for the three types of ratios in systems described by the homogeneous and the inhomogeneous Boltzmann equations is given in the book by Stacey (41). In the present review we formulate GPT for composite functionals. These functionals include the three types of ratios mentioned above as special cases. The result is a unified GPT formulation for each type of system. 

Generalized perturbation theory for two special cases of composite functionals are presented and discussed in some detail GPT for reactivity (Section V,B), and GPT for a detector response in inhomogeneous systems (Section V,E). The GPT formulation for reactivity is equivalent to a high-order perturbation theory, in the sense that it allows for the flux perturbation, GPT for a detector response in inhomogeneous systems 42, 43) is, in fact, the second-order perturbation theory known from other derivations I, 44, 45). These perturbation theory formulations provide the basis for new methods for solution of deep-penetration problems. These methods are reviewed in Section V,E,2. 

Perturbation theory for detector response in inhomogeneous systems provides the foundation for efficient and interesting methods for the solution of deep-penetration problems characterized by a large source-detector distance and a localized geometrical irregularity. 

The classical models of adsorption processes like Langmuir, BET, DR or Kelvin treatments and their numerous variations and extensions, contain several uncontrolled approximations. However, the classical theories are convenient and their usage is very widespread. On the other hand, the aforementioned classical theories do not start from a well - defined molecular model, and the result is that the link between the molecular behaviour and the macroscopic properties of the systems studied are blurred. The more developed and notable descriptions of the condensed systems include lattice models [408] which are solved by means of the mean - field or other non-classical techniques [409]. The virial formalism of low -pressure adsorption discussed above, integral equation method and perturbation theory are also useful approaches. However, the state of the art technique is the density functional theory (DFT) introduced by Evans [410] and Tarazona [411]. The DFT method enables calculating the equilibrium density profile, p (r), of the fluid which is in contact with the solid phase. The main idea of the DFT approach is that the free energy of inhomogeneous fluid which is a function of p (r), can be... 

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