L1 ⚛ L1-319 ⊙ Testnet

GW Approximation for Quasiparticle Energies

Quantum Mechanics · Many-body perturbation theory

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⬇ L1-319.md

# ⚛ L1 Principle — GW Approximation for Quasiparticle Energies **ID:** `L1-319` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Many-body perturbation theory* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** quasiparticle energies > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554080 --- ## 🧠 1. Introduction **GW Approximation for Quasiparticle Energies** is a **nonlinear inverse problem** whose unknown lives in **quasiparticle energies** space, within the **Many-body perturbation theory** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **photoemission** sensing mechanism. The forward operator applies, in order: E · G function operator; E · W screening operator; applies a smooth nonlinear function element-wise; O · quasiparticle operator. Observations are corrupted by additive Gaussian noise. Moderately ill-posed; self-consistent GW (scGW) partially removes G_0W_0 starting-point dependence. ## ⚙ 2. Forward Model Physical chain: **x** → E · G function → E · W screening → Pointwise nonlinearity → O · quasiparticle → **y** (detector). ``` y = `O.quasiparticle` f(·) `E.W_screening` `E.G_function` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.G_function` | E · g function operator | | `E.W_screening` | E · w screening operator | | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.quasiparticle` | O · quasiparticle operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | Many-body perturbation theory | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | quasiparticle_energies | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 10 | | L dag | 4 | ## 📡 4. Measurement Model Moderately ill-posed; self-consistent GW (scGW) partially removes G_0W_0 starting-point dependence. | Metric | Value | |---|---| | Metric | band_gap_error_eV | | Secondary | energy_dispersion_L2_eV | ## 📏 5. Operating Range (Ω) **Center problem class:** `gw_approximation` · **Forward operator:** `GW_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N omega | — | 20 | | Species | — | Si | | N kpoints | — | 8 | | Cutoff ev | — | 400 | | N bands gw | — | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N omega | — | 10 – 200 | | N kpoints | — | 1 – 1000 | | Cutoff ev | — | 200 – 2000 | | N bands gw | — | 20 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** gap error <= 0.07 eV | Metric | Range | |---|---| | Band gap error ev | 0.02 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **band_gap_error_eV**, with κ = `2500` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x82cd9e6737865a0e949c907619b01c3673a8f485b825c68dad90e511e017f853` - **Chain tx hash:** `0xdf4152101dc83ff1b363b6a2ef186a434778a31de966c6964b2e023ce395ae77` - **Chain block:** `41554080` --- ## File Mapping This bundle consists of: `L1-319.md`, `L1-319.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-319.md` | Source of truth — edit this | Human or LLM | | `L1-319.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-319`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-319.md).
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📋 JSON metadata

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  "domain": "Quantum Mechanics",
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  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "electron",
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    "integration_axis": "energy",
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    "sub_domain": "Many-body perturbation theory",
    "title": "GW Approximation for Quasiparticle Energies"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Many-body perturbation theory",
  "title": "GW Approximation for Quasiparticle Energies"
}

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