calculated complex energies in an open-clean chain of finite length. The result we obtain is a polynomial equation which we have been able to solve for long chains using an ansatz for the solution. To the best of our knowledge, this result has never been derived before. We have used a perturbation theory up to the second order where we have derived the first and the second order corrections to the complex energies in terms of Chebyshev polynomials. The first order corrections have been useful to obtain closed form of the statistical results for the scattered complex energies. These results have been further simplified for long chains where we obtain compact results. The asymptotic results have been verified against numerics. Evidently, in the weak disorder limit the perturbation theory predicts nice statistical results. Our results are new in these studies and they could be useful in the further studies of such systems.

It would be interesting to study statistics of resonances in the weak disorder limit for higher dimensional models as well as for the cases when the site energies are not independent random variables but they are correlated with each other [@Izrailev:99]. Besides, there has been growing interest for 