The Anomalous Behaviour of Fermions in a Thin Wire

Motivated by the recent development of insulated nano-tubes and the attempts to develop conducting nano wires in such tubes, we examine the Fermionic behaviour in extremely thin wires. Although the one- dimensional problem has been studied in detail over the years, it is an extreme idealization: We consider the more realistic scenario of thin wires which are nevertheless three dimensional. We show that the assembly of Fermions behaves as if it is below the Fermi temperature, and in the limit of one dimension, in the ground state as well. Thus there are indeed Bosonization features. These conclusions are checked from an independent stand point.