  An existence of predominant symmetrical spin configuration (spin polarised
phase) and "diluted" density of states (pseudo-gap) in a layer under the Fermi
level in a quantum wire is predicted. The condition of cross-over from
non-polarised phase to polarised one was derived. The transition occurs for
sufficiently low electron density in a wire and is accompanied by an acute
decrease of electron density of states near the Fermi level.It may result in a
corresponding decrease of conductance. A similar effect may exist in a
two-dimensional electron gas.
