Quantum correlations and coherence between two particles interacting with a thermal bath

Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath, are studied. The reduced density matrix is solved using the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied, calculating off-diagonal elements of the density matrix, spatiotemporal dispersion, purity and quantum mutual information. We find a characteristic time-scale pointing out when this coherence is maximum. In addition, a Wigner-like distribution in the phase-space (lattice) is introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function also shows a behavior which is in agreement with the time-scale that we have found. A Gaussian distribution for the profile of particles is not obtained, and interference patterns are observed as the result of bath-induced coherence. As the temperature of the bath vanishes, the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord is calculated, to characterize the nature of the correlations.