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Local number variance as a causal handle in the one-dimensional Bose-Hubbard chain

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Zenodo
DOI
10.5281/zenodo.19236689

We test whether the local occupation variance Fi=n^i2n^i2F_i=\langle \hat n_i^2\rangle-\langle \hat n_i\rangle^2 identifies causally effective intervention sites in a one-dimensional open Bose-Hubbard chain under Lindblad dephasing. Additional dephasing at the top-kk highest-FiF_i sites is compared against matched-budget random targeting across 100 independent trials per condition, using exact Lindblad evolution in the fixed-particle-number sector (L6,7,8L\in{6,7,8}, τ1,2,3\tau\in{1,2,3}). The primary sweep reveals three regimes: at J/U=0.12J/U=0.12 targeted intervention is harmful; near J/U0.20J/U\simeq0.20 there is a crossover sensitive to system size and horizon; and at J/U0.30J/U\ge0.30 targeted intervention is reliably beneficial, with 95% confidence intervals above zero at every tested (L,τ)(L,\tau) combination. Controls using disorder, shell-matched permutations, deterministic tilt chains, and extra-dephasing-rate scans show that the effect is not reducible to geometric centrality, shell position, mean occupation, disorder amplitude, or a tuned intervention strength. Because the systems are small enough for exhaustive enumeration, we rank the FiF_i-selected subset against all (Lk)\binom{L}{k} possible intervention subsets; in the positive-pocket regime it lies at the top of the subset-response distribution and the conclusion survives signed, absolute, and redistribution-based target definitions. Finite-difference susceptibility analysis shows that FiF_i is not a local-depletion susceptibility but a redistribution susceptibility: high-FiF_i sites are those where small extra dephasing most strongly perturbs the global occupation pattern. Thus, within the tested finite chains, local number variance functions as a regime-dependent redistribution handle for targeted dephasing.

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