Resonances in one-dimensional Disordered Chain

We study the average density of resonances, $<\rho(x,y)>$, in a semi-infinite disordered chain coupled to a perfect lead. The function $<\rho(x,y)>$ is defined in the complex energy plane and the distance $y$ from the real axes determines the resonance width. We concentrate on strong disorder and derive the asymptotic behavior of $<\rho(x,y)>$ in the limit of small $y$.