  The quark-antiquark potentials are known to be confining in the absence of
the $\bar{q}q$ pair creation. On the other hand, the inter-hadron potentials
vanish at large distance, because the interaction range is limited by the
inverse pion mass. When the $\bar{q}q$ pair creation and annihilation are
switched on, the channel coupling occurs between the quark and hadron degrees
of freedom, modifying the behavior of potentials. In this work, we investigate
the properties of the effective potentials obtained by eliminating one of the
channels. We show that the coupling to the eliminated channel induces a
non-local and energy dependent effective potential, irrespective of the
properties of the transition potential. In addition, when the hadron channel
having continuous scattering eigenstates is eliminated, the resulting
inter-quark potential contains an imaginary part above the threshold to
describe the decay effect into the meson pair.
