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.