  In this work we propose a measure for the quantum discord of
indistinguishable particles, based on the definition of entanglement of
particles given in [H. M. Wiseman et al., Phis. Rev. Lett 91, 097902 (2003)].
This discord of particles is then used to evaluate the quantum correlations in
a system of two identical bosons (fermions), where the particles perform a
quantum random walk described by the Hubbard hamiltonian in a 1D lattice. The
dynamics of the particles is either unperturbed or subject to a classical
environmental noise - such as random telegraph, pink or brown noise. The
observed results are consistent with those for the entanglement of particles,
and we observe that on-site interaction between particles have an important
protective effect on correlations against the decoherence of the system.
