chapter  1
The One-Dimensional Electron Gas
ByGeorge Grüner
Pages 14

The reduction of phase space from three dimensions to one dimension has several important consequences. Both interaction effects and random potentials have a more profound effect in one than in higher dimensions and fluctuations are also more important. The correlation length for models which involve the response of the electron gas to electron-phonon or electron-electron interactions, is related to the correlation length which characterizes the density fluctuations of the one-dimensional electron gas. The particular topology of the Fermi surface leads to a response to an external perturbation which is dramatically different from that obtained in higher dimensions. The quasi-one-dimensional character of the Fermi surface can be modeled by including a dispersion in the direction perpendicular to the direction along which the response function was evaluated. Because of the reduction of phase space, one-dimensional systems are unstable against fluctuations.