Dynamics of quantum resources under noisy spatial deformation of identical particles

We present a microscopic derivation of a master equation for two bosonic qubits tunneling between spatially separated modes under local dephasing, described by a Lorentzian spectrum. The resulting time-local equation reveals intrinsic non-Markovian features. When the bath central frequency is resonant with the tunneling amplitude, dephasing can drive the system toward a correlated steady state that sustains coherence and entanglement, as opposed to complete decoherence predicted by white noise models. These results provide a rigorous foundation for pure dephasing in bosonic tunneling systems and demonstrate how structured noise can actively generate steady-state quantum correlations.