Targeted Dephasing as a Causal Handle on Local Occupation Loss in an Open Bose–Hubbard Chain

In an open one-dimensional Bose–Hubbard chain with Lindblad dephasing, targeted additional dephasing at sites of high local occupation variance produces more future local occupation loss than matched-budget random targeting in the J/U = 0. 30–0. 40 regime. The effect is positive and robust at J/U ∈ 0. 30, 0. 40 across three time horizons (τ ∈ 1, 2, 3) and two chain lengths (L ∈ 6, 7), with bootstrap confidence intervals excluding zero at every tested point in that range. The lowest tested coupling (J/U = 0. 12) is uniformly negative, while J/U = 0. 20 is transitional and size-sensitive. The observed spatial response is more consistent with nonlocal redistribution of occupation loss than with a purely local-instability account. All results are computed by exact Lindblad evolution in the fixed-particle-number sector; no approximations are used.