Variance as an intervention-relative control selector in an open Bose–Hubbard chain

Kunal Bhatia — Independent Researcher, Heidelberg, Germany ORCID: 0009-0007-4447-6325

Companion code and data for an exact-Lindblad study of the 1D open Bose–Hubbard chain. The repository now hosts two related manuscripts plus a supporting reanalysis; all simulation is exact (no Trotter, stochastic unravelling, or mean field), restricted to small chains ($L\le 8$).

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Two tracks

Track	Manuscript	Question	Status
1. Predictive	paper.tex / paper.pdf	Does targeting the highest-variance sites with extra dephasing change future occupation loss more than matched-budget random targeting?	submitted to Physical Review A; declined at editorial assessment (insufficient significance / broad interest)
2. Mechanism	paper_v2.tex / paper_v2.pdf	Why does it work, and does the operative control variable depend on the intervention class?	in preparation
(supporting)	bh_reanalysis/	Observer-geometry / principal-angle reanalysis of the same outputs	internal, pre-registered

paper_v2.tex is the current mechanism manuscript and the response to that rejection; paper.tex is preserved as the submitted (declined) version. paper_expanded_may6.tex is an earlier expanded draft kept only as reference material.

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The result in brief (Track 2)

For a selected site set $S$ define the directed self-drain $D_S(\tau)=-\sum_{i\in S}\Delta\langle\hat n_i\rangle(\tau)$ ($D_S>0$ ⇒ the selected sites lose occupation). Because the dephasing dissipator conserves each $\langle\hat n_i\rangle$ exactly, particle-number continuity makes $D_S$ the time-integrated net outward current of $S$. The findings:

• The handle works only in the directed self-draining regime; the burn-in current divergence of $S$ predicts it (Spearman $\rho\approx0.9$ at $L=6,7,8$), and the $J/U$ crossover is a current reversal (inward/fill → outward/drain).
• The earlier "redistribution susceptibility" explanation is non-discriminating ($\rho\approx0$ with success) and is retired; geometry is a correlate, not fundamental.
• The operative selector is intervention-relative:

intervention	conserves $N$?	coherent?	operative selector
dephasing	yes	no	$F_i$ (reads pre-existing current)
detuning	yes	yes	$F_i$ (imposes current)
local loss	no	no	$\langle n_i\rangle$ (direct removal)
bond hopping mod.	yes	yes	site-level $F_i$ (not bond)

The boundary between the two selectors is transport-modulation vs. particle-removal (equivalently, particle-number conservation).

The original predictive thesis (Track 1) — top-$F_i$ targeting beats matched random in the "positive pocket" $J/U\ge0.30$, robust across $L=6,7,8$ and the disorder/tilt/shell-permutation controls — remains intact and is the content of paper.tex.

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Repository map

Everything lives at the top level (flat) plus bh_reanalysis/ and outputs/. Grouped by purpose:

Simulation engine

• bh.py — exact-Lindblad Bose–Hubbard engine and the full experiment battery (primary sweep, disorder/selector sweep, shell-perm, inhomogeneous tilt, gamma scan). CLI-driven (--help).
• bh_hardening.py — hardening battery: exhaustive subset ranking, susceptibility, burn-in sensitivity, $n_{\max}$ truncation check. Defines build_condition/evolve_with_extra reused below.

Mechanism program (Track 2) — in mechanism/; each writes CSVs to outputs/mechanism_pilot/ (run from root, PYTHONPATH=.)

• mechanism_pilot.py [L] — response-kernel handle + size scaling ($L=6,7,8$).
• current_mechanism.py [L], current_symbreak.py — current/continuity diagnostic ($C_S^{\rm burn}!\to!D_S$).
• symbreak_diag.py tilt|disorder — geometry separation under symmetry breaking (dephasing).
• detune_probe.py, symbreak_detune.py tilt|disorder, finish_detune_disorder.py — coherent detuning.
• stage0_loss.py, loss_pilot.py, loss_symbreak.py — multi-$N$ local loss (machinery + pilots).
• bond_pilot.py — per-bond-$J$ hopping modulation (site-vs-bond control).
• mechanism_parity_check.py — sparse vs dense Liouvillian parity ($\sim10^{-15}$).
• make_paper_assets.py — regenerates paper_v2 figures, tables, and key_numbers.json from the CSVs.

Manuscripts & bibliography

• paper.tex/paper.pdf (Track 1), paper_v2.tex/paper_v2.pdf (Track 2), paper_expanded_may6.tex (reference draft), refs.bib, cover_letter.txt.

Records — in notes/ (source-of-truth, human-readable)

• notes/CLAIM_EVIDENCE_MAP.md — start here for reproducibility: every paper_v2 claim → figure/table → source CSV → verified value.
• MECHANISM_STATE.md — full chronological mechanism log (steps 1–4; what is earned/retired).
• CLAIM_STATUS.md — one-page milestone. PAPER_OUTLINE.md — rewrite plan.
• LOSS_PILOT_PREREG.md, BOND_HOPPING_PREREG.md — pre-registrations.

Tests & build

• test_bh.py, test_new_experiments.py — unit tests (run first).
• build.sh — compile the papers. run_all.sh — the original AWS/EC2 batch campaign script.

Data (outputs/)

• mechanism_pilot/ — Track-2 result CSVs (+ paper_v2/ figures, tables, key_numbers.json).
• bh_hardening/ — hardening CSVs/figures. checkpoints/ — per-condition sweep checkpoints (L8/L9 tracked; the rest reproducible via bh.py --resume). figures/, tables/, data/ — Track-1 paper assets.

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Reproducing the results

Requirements: Python 3.11+, numpy scipy pandas matplotlib tqdm. Run from the repo root with PYTHONPATH=. so the mechanism/ scripts find bh.py/bh_hardening.py at the root.

python3 -m pytest test_bh.py test_new_experiments.py -q   # tests first

Track 2 (mechanism) — fast, exact, laptop-scale. Each line writes the CSV the paper draws from:

Result (paper_v2)	Command — prefix PYTHONPATH=. python3 mechanism/	Output CSV
Handle + size scaling	mechanism_pilot.py 6 (and 7, 8)	pilot_results_L{6,7,8}.csv
Current/continuity mechanism	current_mechanism.py 6 (and 7,8)	current_mech_L{6,7,8}.csv
Current under symmetry breaking	current_symbreak.py	current_symbreak_{tilt,disorder}.csv
Geometry separation (dephasing)	symbreak_diag.py tilt / disorder	symbreak_{tilt,disorder}.csv
Detuning (clean + sign)	detune_probe.py	detune_probe_L6.csv
Detuning (symmetry-broken)	symbreak_detune.py tilt / disorder 10	symbreak_detune_{tilt,disorder}.csv
Loss (validate → pilots)	stage0_loss.py; loss_pilot.py; loss_symbreak.py	loss_pilot_L6.csv, loss_symbreak_mini.csv
Bond control	bond_pilot.py	bond_pilot_L6.csv
Figures + tables + key numbers	make_paper_assets.py	outputs/paper_v2/…

Then compile: pdflatex paper_v2 && bibtex paper_v2 && pdflatex paper_v2 && pdflatex paper_v2. The mechanism pilots run in seconds–minutes each; sparse/dense agreement is checked by mechanism_parity_check.py. The loss disorder sweep self-checkpoints per realization (finish_detune_disorder.py shows the resumable pattern).

Track 1 (predictive paper). The primary sweep, disorder/selector, shell-perm, inhomogeneous, and gamma-scan experiments are driven by bh.py (see --help); the hardening battery (exhaustive ranking, susceptibility, burn-in, $n_{\max}$) by bh_hardening.py. The full campaign was run on AWS/EC2 (run_all.sh) with per-condition checkpoints synced to S3 and pulled into outputs/checkpoints/.

System parameters (both tracks)

1D Bose–Hubbard, open BC, half-filling $N=\lfloor L/2\rfloor$, $n_{\max}=3$; $L\in{6,7,8}$ ($D=56,84,322$); baseline $\gamma=0.1$, $\gamma_{\rm extra}=0.5$, burn-in $t=5$, horizons $\tau\in{1,2,3}$; dense for $D\le84$, sparse CSR above (mechanism scripts force sparse for $L\ge7$). Seed 20260325.

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What is and is not claimed

• Earned: the intervention-relative selector map above, the directed-self-drain/current mechanism, and its size support to $L=8$ — all from exact Lindblad evolution, with every headline number independently re-verified (see CLAIM_EVIDENCE_MAP.md).
• Not claimed: the thermodynamic limit, larger $L$, a universal control law, all intervention types, particle injection, or laboratory realization. The $J/U\approx0.20$ feature is a finite-size dynamical crossover, not the Mott–superfluid transition.
• The observer-geometry reanalysis's T1 "predictive–causal dissociation" is retired as a finding (a self-correlation artifact; honest rate $\sim0.52$, not $\sim0.90$); only its thermalization-convergence (T4) and scoring-rule-fork (T5) outcomes are kept as supporting.

Branches & provenance

main is the integrated state. pre-integration-2026-06-06 tags the pre-merge restore point. bh-reanalysis-archive holds the reanalysis history; claude/happy-yalow-455c61 is the original (orphaned) worktree branch that also contains the expanded draft.

License

See LICENSE.