  Bound states and their influence on the dynamics of an one-dimensional
tight-binding system subject to environments are studied in this paper. We
identify specifically three kinds of bound states. The first is a discrete
bound state (DBS), of which the energy level exhibits a gap from the continuum.
The DBS exhibits the similar features of localization as the edge states in the
system and thus can suppress the decay of system. The second is a bound state
in the continuum (BIC), which can suppress the system decay too. It is found
that the BIC is intimately connected to the edge mode of the system since both
of them show almost the same features of localization and energy. The third one
displays a large gap from the continuum and behaves extendible (not localized).
Moreover the population of the system on this state decays partly but not all
of them does. This is different from the two former bound states. The time
evolution of a single excitation in the system is studied in order to
illustrate the influence of the bound states. We found that both DBS and BIC
play an important role in the time evolution, for example, the excitation
becomes localized and not decay depending on the overlap between the initial
state and the DBS or BIC. Furthermore we observe that the single excitation
takes a long-range hopping when the system falls into the regime of strong
localizations. This feature can be understood as the interplay of system
localizations and the bath-induced long-range correlation.
