Book contents
- Frontmatter
- 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
- Appendices
- References
- Index
5 - Linear response of an interacting electron liquid
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- 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
- Appendices
- References
- Index
Summary
Introduction and guide to the chapter
Linear response functions contain a wealth of information about the physical properties of a many-body system. In the case of the electron liquid, for example, the density–density response function provides a unified framework for the understanding of different phenomena such as static screening, effective interaction, collective modes, electron energy loss spectra (inelastic scattering of electrons), and Raman spectra (inelastic scattering of photons). The spin–spin response function provides the corresponding information for the spin density fluctuations as probed, for example, by cross-polarized Raman scattering experiments, in which the incident and scattered photon have perpendicular polarizations, or by spin-flip electron energy loss spectroscopy, in which the incoming and outgoing electrons have opposite spin orientations.
As we have seen, the Hartree–Fock approximation describes each electron as an independent particle moving in a self-consistent field generated by all the other electrons. There is no correlation between this self-consistent field and the instantaneous position of the electron. Reality is however quite different: whenever an electron moves, it acts on the surrounding electrons, causing a collective disturbance which eventually feeds back on its own motion. In order to study these effects we need, first of all, to learn how the electron liquid as a whole responds to disturbances caused by the charge, the spin, and the current of a single electron. The linear response theory of Chapter 3 provides the natural framework for this description. Strictly speaking, the linear response functions describe the readjustments of the electronic density, spin, or current, in response to externally controlled fields.
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- Information
- Quantum Theory of the Electron Liquid , pp. 188 - 274Publisher: Cambridge University PressPrint publication year: 2005