  In the paper, we are concerned with the nonlinear Cauchy problem on the
Vlasov-Poisson-Landau/Boltzmann system around global Maxwellians in torus or
finite channel. The main goal is to establish the global existence and large
time behavior of small amplitude solutions for a class of low regularity
initial data. The molecular interaction type is restricted to the case of hard
potentials for two classical collision operators because of the effect of the
self-consistent forces. The result extends the one by Duan-Liu-Sakamoto-Strain
[{\it Comm. Pure Appl. Math.} 74 (2021), no.~5, 932--1020] for the pure
Landau/Boltzmann equation to the case of the VPL and VPB systems.
