We consider a system composed of two distinct spatial regions, populated by two-component bosons coupled through a tunneling process. Local dephasing noise acts independently on each region, enabling competition between coherent dynamics and decoherence. We present an analytic microscopical derivation of the corresponding Lindblad master equation, taking into account the full system-environment evolution and verify its validity against the numerical solution of the full system, computed through the pseudo-mode method. We demonstrate how the commonly-used phenomenological master equation emerges as a short-time limit of the full one. We finally explore how dephasing affects known two-particle indistinguishability-based scenarios, namely Hong-Ou-Mandel interference and entanglement generation. In particular, we show that simultaneous deformation and dephasing can produce rich, nontrivial dynamics, including persistent quantum correlations in long-time steady states.
Ferrara et al. (Sat,) studied this question.