  We analyze the effect that the Coulomb interaction has on the edge
excitations of an electron gas confined in a bar of thickness $W$, and in
presence of a magnetic field corresponding to filling factor 1 Quantum Hall
effect. We find that the long-range interaction between the edges leads the
system to a ground state with a quasi-long range order, similar to a Charge
Density Wave. The spectral density of states vanishes at zero frequency, and
increases with frequency faster than any power law, being the conductance of a
infinite long system zero.
