L1 ⚛ L1-320 ⊙ Testnet

Bethe-Salpeter Equation for Excitons

Quantum Mechanics · Optical excitations from GW+BSE

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⬇ L1-320.md

# ⚛ L1 Principle — Bethe-Salpeter Equation for Excitons **ID:** `L1-320` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Optical excitations from GW+BSE* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** exciton spectrum > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554080 --- ## 🧠 1. Introduction **Bethe-Salpeter Equation for Excitons** is a **nonlinear inverse problem** whose unknown lives in **exciton spectrum** space, within the **Optical excitations from GW+BSE** sub-domain of **Quantum Mechanics**. Measurements consist of photons collected by an optical detector via a **optical absorption** sensing mechanism. The forward operator applies, in order: E · GW bands operator; E · kernel K eh operator; computes eigen-pairs of a linear operator; O · absorption operator. Observations are corrupted by additive Gaussian noise. Tamm-Dancoff approximation often used; scaling as N^4 limits size. ## ⚙ 2. Forward Model Physical chain: **x** → E · GW bands → E · kernel K eh → O · absorption → **y** (detector). ``` y = `O.absorption` `E.kernel_K_eh` `E.GW_bands` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.GW_bands` | E · gw bands operator | | `E.kernel_K_eh` | E · kernel k eh operator | | `O.absorption` | O · absorption operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `E.eigensolve` | Computes eigen-pairs of a linear operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | Optical excitations from GW+BSE | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | exciton_spectrum | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 10 | | L dag | 4.2 | ## 📡 4. Measurement Model Tamm-Dancoff approximation often used; scaling as N^4 limits size. | Metric | Value | |---|---| | Metric | exciton_binding_error_eV | | Secondary | optical_spectrum_L2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `bethe_salpeter` · **Forward operator:** `BSE_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N kpoints | — | 64 | | N cv pairs | — | 500 | | Omega range ev | — | 0 – 10 | | Dielectric screening | — | static | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N kpoints | — | 8 – 10000 | | N cv pairs | — | 50 – 50000 | | Dielectric screening | — | static, dynamic | ## 🎯 6. Tolerance (ε) **Center tolerance:** binding error <= 0.05 eV | Metric | Range | |---|---| | Exciton binding error ev | 0.01 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **exciton_binding_error_eV**, with κ = `3000` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x636afa279a36289b70b868a82409af8e16d1ae7c4f7cce219babbc46858b4b62` - **Chain tx hash:** `0x8875687ca7bf4a1a6d61606f29dc32a63abb12b369d806032eaaadce12c1fc50` - **Chain block:** `41554080` --- ## File Mapping This bundle consists of: `L1-320.md`, `L1-320.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-320.md` | Source of truth — edit this | Human or LLM | | `L1-320.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 `L1-320`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-320.md).
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📋 JSON metadata

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  "chain_block": 41554080,
  "chain_hash": "0x636afa279a36289b70b868a82409af8e16d1ae7c4f7cce219babbc46858b4b62",
  "chain_tx_hash": "0x8875687ca7bf4a1a6d61606f29dc32a63abb12b369d806032eaaadce12c1fc50",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
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    "regime": "Tamm-Dancoff approximation often used; scaling as N^4 limits size.",
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  },
  "physics_fingerprint": {
    "L_DAG": 4.2,
    "carrier": "photon",
    "difficulty_delta": 10,
    "domain": "Quantum Mechanics",
    "integration_axis": "energy",
    "noise_model": "gaussian",
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    "sensing_mechanism": "optical_absorption",
    "solution_space": "exciton_spectrum",
    "sub_domain": "Optical excitations from GW+BSE",
    "title": "Bethe-Salpeter Equation for Excitons"
  },
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    "allowed_omega_dimensions": [
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        "N_kpoints": 64,
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        "dielectric_screening": "static"
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        1.0
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    },
    "omega_bounds": {
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        50000
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      "N_kpoints": [
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      ],
      "dielectric_screening": [
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        "dynamic"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Optical excitations from GW+BSE",
  "title": "Bethe-Salpeter Equation for Excitons"
}

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