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Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.

Fermi liquid theory --- Fermi surfaces --- Hartree-Fock approximation --- Many-body problem --- Quantum field theory --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Hartree approximation --- Hartree-Fock-Slater approximation --- Approximation theory --- Atoms --- Energy-band theory of solids --- Self-consistent field theory --- Surfaces, Fermi --- Electrons --- Free electron theory of metals --- Quantum statistics --- Landau Fermi liquid theory --- Landau theory of Fermi liquids --- Landau's theory of Fermi liquids --- Fermi liquids

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The book is dedicated to the application of self-consistent methods to the solution of static and dynamic problems of the mechanics and physics of composite materials. The effective elastic, electric, dielectric, thermo-conductive and other properties of composite materials reinforced by ellipsoidal, spherical multi-layered inclusions, thin hard and soft inclusions, short fibers and unidirected multi-layered fibers are considered. Explicit formulas and efficient computational algorithms for the calculation of the effective properties of the composites are presented and analyzed. The method of the effective medium and the method of the effective field are developed for the calculation of the phase velocities and attenuation of the mean (coherent) wave fields propagating in the composites. The predictions of the methods are compared with experimental data and exact solutions for the composites with periodical microstructures. The book may be useful for material engineers creating new composite materials and scholars who work on the theory of composite and non-homogeneous media.

Self-consistent field theory. --- Inhomogeneous materials. --- Composite materials. --- Engineering mathematics. --- Composite materials --- Inhomogeneous materials --- Mechanical properties. --- Engineering --- Engineering analysis --- Mathematical analysis --- Composites (Materials) --- Multiphase materials --- Reinforced solids --- Solids, Reinforced --- Two phase materials --- Materials --- Heterogeneous materials --- Inhomogeneous media --- Media, Inhomogeneous --- Matter --- SCF theory --- Self consistent field method --- Self consistent fields --- Field theory (Physics) --- Molecular orbitals --- Mathematics --- Materials. --- Mechanics. --- Mechanics, Applied. --- Surfaces (Physics). --- Materials Science, general. --- Solid Mechanics. --- Structural Materials. --- Ceramics, Glass, Composites, Natural Materials. --- Characterization and Evaluation of Materials. --- Classical Electrodynamics. --- Physics --- Surface chemistry --- Surfaces (Technology) --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Materials science. --- Structural materials. --- Ceramics. --- Glass. --- Composites (Materials). --- Optics. --- Electrodynamics. --- Light --- Amorphous substances --- Ceramics --- Glazing --- Ceramic technology --- Industrial ceramics --- Keramics --- Building materials --- Chemistry, Technical --- Clay --- Architectural materials --- Architecture --- Building --- Building supplies --- Buildings --- Construction materials --- Structural materials --- Material science --- Physical sciences