Quantum Theory of the Electron Liquid

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.

1. Introduction to the electron liquid; 2. The Hartree-Fock approximation; 3. Linear response theory; 4. Linear response of independent electrons; 5. Linear response of an interacting electron liquid; 6. The perturbative calculation of linear response functions; 7. Density functional theory; 8. The normal Fermi liquid; 9. The one-dimensional electron gas and the Luttinger liquid; 10. The two-dimensional electron gas at high magnetic field.