Tunnel density of states in a Luttinger constriction

We study Luttinger constriction that is a finite region of interacting electrons adiabatically connected to the reservoirs of non-interacting electrons. We have shown that, in contrast to an infinite Luttinger liquid, the density of states (DOS) remains finite at the Fermi surface although it is strongly suppressed in comparison with the non-interacting value. The finite-size effects give rise to an additional staircase structure in the energy dependence of the DOS at higher energies.