  The robustness of quantum transport under various perturbations is analyzed
in disordered interacting many-body systems, which are constructed from the
embedded Gaussian random matrix ensembles (EGEs). The transport efficiency can
be enhanced drastically, if centrosymmetry (csEGE) is imposed. When the csEGE
is perturbed with an ordinary EGE, the transport efficiency in the optimal
cases is reduced significantly, while in the suboptimal cases the changes are
less pronounced. Qualitatively the same behavior is observed, when parity and
centrosymmetry are broken by block perturbations. Analyzing the influence of
the environment coupling, optimal transport is observed at a certain coupling
strength, while too weak and too strong coupling reduce the transport. Taking
into account the effects of decoherence, in the EGE the transport efficiency
approaches its maximum at a finite nonzero decoherence strength
(environment-assisted transport). In the csEGE the efficiency decays
monotonically with the decoherence but is always larger than in the EGE.
