verify our analytical results. This will be followed by the conclusion in Sec. VII.

![A one-dimensional disordered chain with $N$ sites, represented in the figure by black dots, is coupled to a lead. Open circles represent sites of the lead. The outgoing plane wave is shown by the arrow where $0<\Re\{\tilde{k}\}<\pi$ and $\Im \{\tilde{k}\}<0$, so that it propagates left in the lead and its amplitude grows in the lead.[]{data-label="System"}](system.eps){width="50.00000%"}

Model and Its Effective Hamiltonian
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A discrete tight-binding one dimensional chain of length $N$ (shown by positive integers, $n=1,\,2,...,\,N$, used for indexing the sites of the chain in Fig. \[System\]) is connected to an outer world (represented by a perfect lead which sites are shown by a zero and negative integers, $n=0,\,-1,\,-2,...$). Each site of the chain has the site energy $\epsilon_{n}$ where $\epsilon_{n}$ are statistically independent random variables chosen from some symmetric distribution. Each nearest neighbor site of the chain as well as of the lead is coupled by a hopping amplitude $t$. The hopping amplitude for the pair $n=0$ and $n=1$ is $t'$ which takes values from $t'=0$ (closed chain) to $t'=t$ (fully coupled chain). With this hopping, a particle, which is initially located somewhere in the chain, 