In this chapter, we study absorption semigroups \(\left( U_{V}(t)\right) _{t\geqslant 0}\) , a class of \(C_{0}\) -semigroups on abstract \(L^{1}\) -spaces formally generated by \(T_{V}=T-V\) , where T is the generator of a substochastic \(C_{0}\) -semigroup \(\left( U(t)\right) _{t\geqslant 0}\) and V is an unbounded measurable function bounded from below. By exploiting a specific contractive property of the operator \(V\left( \lambda -T_{V}\right) ^{-1}\) , valid in \(L^{1}\) -spaces, along with the confining nature of the potential V and a “local weak compactness” condition on the resolvent \(\left( \lambda -T\right) ^{-1}\) , we establish the existence of a local spectral gap at the boundary of the spectrum of \(T_{V}\) . We also present a more robust approach that applies in all \(L^{p}\) -spaces, does not rely on contractivity, and yields a stronger result: when the semigroup \(\left( U(t)\right) _{t\geqslant 0}\) is “locally compact”, the absorption semigroup possesses \(\left( U_{V}(t)\right) _{t\geqslant 0}\) a spectral gap.