  Quantum correlations between two free spinless dissipative distinguishable
particles (interacting with a thermal bath) are studied analytically using the
quantum master equation and tools of quantum information. Bath-induced
coherence and correlations in an infinite-dimensional Hilbert space are shown.
We show that for temperature T > 0 the time-evolution of the reduced density
matrix cannot be written as the direct product of two independent particles. We
have found a time-scale that characterizes the time when the bath-induced
coherence is maximum before being wiped out by dissipation (purity, relative
entropy, spatial dispersion, and mirror correlations are studied). The Wigner
function associated to the Wannier lattice (where the dissipative quantum walks
move) is studied as an indirect measure of the induced correlations among
particles. We have supported the quantum character of the correlations by
analyzing the geometric quantum discord.
