Configuration-Dependent Classicalisation in a Two-Sector Collision Model

We study a bipartite quantum system comprising two coupled Fock-space sectors evolved under a collision model with environment-reset dynamics. The two sectors interact via a beam-splitter Hamiltonian that preserves total excitation number. At each discrete time step, the system undergoes unitary evolution followed by a partial trace over a fresh environmental ancilla, defining a completely positive trace-preserving (CPTP) map. We establish five results. First, the system possesses a diagonal attractor, robust across the entire parameter space tested (600 independent runs spanning a three- dimensional Latin hypercube): the density matrix converges to a state diagonal in the joint number basis. Second, the coherence persistence time obeys a power-law scaling τ = A Cb with b = −0.257 ± 0.020 and R2 = 0.77, where C = γ · ns · N depends on the coupling strength γ, the second-sector excitation number ns, and the number of interaction cycles N. Third, a sharp coupling threshold γ ≥ 1/N separates a regime of frozen asymmetry from one of reliable convergence. Fourth, in the weak-coupling limit, the discrete dynamics reduce to the standard GKSL master equation, reproducing the known γ2 scaling of decoherence rates. Fifth, the dependence on internal configuration ns constitutes a falsifiable prediction that distinguishes this model from standard environment-only decoherence.