Quantum theory of the electron liquid / Gabriele Giuliani, Giovanni Vignale.

Includes bibliographical references (pages 742-764) and index.

Print version record.

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.

Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 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 Electrons in one dimension and the Luttinger liquid; 10 The two-dimensional electron liquid at high magnetic field; Appendix 1: Fourier transform of the coulomb interaction in low dimensional systems

Appendix 2: Second-quantized representation of some useful operatorsAppendix 3: Normal ordering and Wick's theorem; Appendix 4: The pair correlation function and the structure factor; Appendix 5: Calculation of the energy of a Wigner crystal via the Ewald method; Appendix 6: Exact lower bound on the ground-state energy of the jellium model; Appendix 7: The density-density response function in a crystal; Appendix 8: Example in which the isothermal and adiabatic responses differ; Appendix 9: Lattice screening effects on the effective electron-electron interaction

Appendix 10: Construction of the STLS exchange-correlation fieldAppendix 11: Interpolation formulas for the local field factors; Appendix 12: Real space-time form of the noninteracting Green's function; Appendix 13: Calculation of the ground-state energy and thermodynamic potential; Appendix 14: Spectral representation and frequency summations; Appendix 15: Construction of a complete set of wavefunctions with a given density; Appendix 16: Meaning of the highest occupied Kohn-Sham eigenvalue in metals; Appendix 17: Density functional perturbation theory

Appendix 18: Density functional theory at finite temperatureAppendix 19: Completeness of the bosonic basis set for the Luttinger model; Appendix 20: Proof of the disentanglement lemma; Appendix 21: The independent boson theorem; Appendix 22: The three-dimensional electron gas at high magnetic field; Appendix 23: Density matrices in the lowest Landau level; Appendix 24: Projection in the lowest Landau level; Appendix 25: Solution of the independent boson model; References; Index

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