Solid reasons to go with the flow

Quantum Theory of the Electron Liquid. First edition
December 2, 2005

A good book for an academic condensed matter theorist," was how one of the UK's leading industrial condensed matter theorists summarised this book to me after browsing it for a few moments.

The publisher says it is intended for graduate students in physics, electrical engineering and quantum chemistry, as well as for practising researchers in those areas. I believe it would also be of interest to materials modellers, with a whole chapter devoted to density functional theory. It assumes a strong underlying knowledge of condensed matter theory - at least to the level of such classics as Charles Kittel's Introduction to Solid State Physics - and fluency in the mathematical tools of solid-state quantum theory.

Enhancing its usefulness for a graduate lecture course, there are problems at the end of each chapter. There are 25 appendices, starting with the Fourier transform of the coulomb interaction in low-dimensional systems and ending with the solution of the independent boson model.

Two regimes of the electron liquid are distinguished. In the weak coupling regime, the kinetic energy rules the physics and the system remains qualitatively similar to a non-interacting gas. In the strong coupling regime, the potential energy dominates and the liquid displays the collective behaviour characteristic of a crystal.

Quantum Theory of the Electron Liquid identifies as one of the most useful concepts in condensed matter physics the Landau-Fermi liquid concept, in which there is a continuous evolution from the low-energy spectrum of a non-interacting system as the interaction is switched on with no change in the volume of the Fermi sphere, but a discontinuity of momentum occupation numbers as the wave vector crosses the Fermi surface.

There is a temptation in such a textbook to describe what can be described, rather than what is relevant for experimental science and technology.

Luttinger liquid behaviour crops up again and again, though the only experiments mentioned involve the tunnelling of electrons into the edges of a two-dimensional electron liquid in GaAs quantum wells. There is a hope expressed that quantum wires that exhibit Luttinger liquid behaviour will eventually be realised, but no discussion of why you should want them, and no evaluation of the growing evidence for Luttinger liquid behaviour in single-walled carbon nanotubes. There are attempts to relate theory to what is possible in the laboratory, with pictures of a GaAs quantum wire and a carbon nanotube, and a beautiful micrograph of Friedel-like oscillations on a copper surface.

This book contains a wealth of information that will repay diligent study, much of it not to be found together in any other graduate textbook. It could provide a skilled tutor with a textbook for an advanced graduate course in condensed matter theory, though it would need to be supplemented by books covering topics omitted here, such as strongly correlated systems and the role of the electron liquid in the bonding of solids.

Andrew Briggs is professor of nanomaterials, Oxford University.

Quantum Theory of the Electron Liquid. First edition

Author - Gabriele F. Giuliani and Giovanni Vignale
Publisher - Cambridge University Press
Pages - 777
Price - £50.00
ISBN - 0 521 82112 6

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