Electronic Systems in d = 1

Abstract

In this chapter we undertake the general description of electrons in one dimension. There exist systems which are actually one-dimensional, as is the case of polyacetilene[1], and others which may be considered “quasi-one-dimensional”, i. e. that show conduction properties in a prefered direction. This is the case of the well-known organic charge-transfer compounds[2]. The study of electronic properties in one dimension is not, therefore, purely academic. This is also supported by the relevance of these systems in the investigation of the so-called “quantum wires” [3] and by the increasing evidence that the edge excitations in the fractional quantum Hall effect are effectively that of a one-dimensional liquid [4].