pith:RREVMAP2
Electrostatics in semiconducting devices II: Solving the Helmholtz equation
Mapping the self-consistent electrostatic problem to a non-linear Helmholtz equation permits provably convergent iterations that reach the exact solution in one or two steps.
arxiv:2507.03131 v5 · 2025-07-03 · cond-mat.mes-hall · physics.comp-ph
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Claims
We show that one can build iterative schemes that are provably convergent by constructing a convex functional whose minimum is the seeked solution of the NLH problem. In a second step, the approximation is lifted and the exact solution of the initial problem found by iteratively updating the NLH problem until convergence. We show empirically that convergence is achieved in a handfull, typically one or two, iterations.
The self-consistent quantum-electrostatic problem can be mapped onto the Non-Linear Helmholtz equation at the cost of only a small error that is later removed by iterative lifting to the exact solution.
Maps the quantum-electrostatic self-consistency problem to a non-linear Helmholtz equation, enabling construction of a convex functional for provable convergence that lifts to the exact solution in typically one or two iterations.
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| First computed | 2026-06-19T16:10:30.357987Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
8c495601fab546338412d460e4c07a76c5bf07f05435debbdb71735194338df0
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· · · · ·Agent API
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curl -sH 'Accept: application/ld+json' https://pith.science/pith/RREVMAP2WVDDHBAS2RQOJQD2O3 \
| jq -c '.canonical_record' \
| python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8c495601fab546338412d460e4c07a76c5bf07f05435debbdb71735194338df0
Canonical record JSON
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"submitted_at": "2025-07-03T19:14:37Z",
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