L1 ⚛ L1-496 ⊙ Testnet

Quantum Well and Quantum Dot Electronic Structure

Semiconductor Physics · Confined electronic states

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⬇ L1-496.md

# ⚛ L1 Principle — Quantum Well and Quantum Dot Electronic Structure **ID:** `L1-496` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Semiconductor Physics — *Confined electronic states* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** wavefunctions energies of confined states > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554142 --- ## 🧠 1. Introduction **Quantum Well and Quantum Dot Electronic Structure** is a **nonlinear inverse problem** whose unknown lives in **wavefunctions energies of confined states** space, within the **Confined electronic states** sub-domain of **Semiconductor Physics**. Measurements consist of electrons collected by an electron detector via a **optical spectroscopy PL absorption** sensing mechanism. The forward operator applies, in order: E · strain operator; E · kp Hamiltonian operator; a fixed-point or gradient iteration on the unknown; O · states transitions operator. Observations are corrupted by additive Gaussian noise. Well-posed; inversion for composition/strain from PL is ill-conditioned (multiple compositions produce same transition). ## ⚙ 2. Forward Model Physical chain: **x** → E · strain → E · kp Hamiltonian → O · states transitions → **y** (detector). ``` y = `O.states_transitions` `E.kp_Hamiltonian` `E.strain` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.strain` | E · strain operator | | `E.kp_Hamiltonian` | E · kp hamiltonian operator | | `O.states_transitions` | O · states transitions operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Semiconductor Physics | | Sub domain | Confined electronic states | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | wavefunctions_energies_of_confined_states | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 5 | | L dag | 3.6 | ## 📡 4. Measurement Model Well-posed; inversion for composition/strain from PL is ill-conditioned (multiple compositions produce same transition). | Metric | Value | |---|---| | Metric | energy_error_meV | | Secondary | oscillator_strength_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `qdot_electronic_inversion` · **Forward operator:** `kp_schrodinger_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 4 | | Basis n | N | 8 | | Size nm | nm | 20 | | Geometry | — | InGaAs_QD_on_GaAs | | Strain pct | — | 7 | | Composition in | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 4 – 300 | | Basis n | N | 4 – 20 | | Size nm | nm | 2 – 100 | | Strain pct | — | 0 – 10 | | Composition in | — | 0.05 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** E_1 error <= 2 meV | Metric | Range | |---|---| | Energy error mev | 0.5 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **energy_error_meV**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8a7ba3f45d743244510b8a33be243539028ae9e9f5b48e572c16a27730f35a61` - **Chain tx hash:** `0xbee99ef9c7180d1b64d7583953b28f2cb05f2c5a5c7d258650ded255931ae0a4` - **Chain block:** `41554142` --- ## File Mapping This bundle consists of: `L1-496.md`, `L1-496.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-496.md` | Source of truth — edit this | Human or LLM | | `L1-496.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 `L1-496`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-496.md).
Regenerate L1-496.json so every field matches the Markdown.
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📋 JSON metadata

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  "artifact_id": "L1-496",
  "chain_block": 41554142,
  "chain_hash": "0x8a7ba3f45d743244510b8a33be243539028ae9e9f5b48e572c16a27730f35a61",
  "chain_tx_hash": "0xbee99ef9c7180d1b64d7583953b28f2cb05f2c5a5c7d258650ded255931ae0a4",
  "domain": "Semiconductor Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "energy_error_meV",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "observable_profile": {
    "metric": "energy_error_meV",
    "regime": "Well-posed; inversion for composition/strain from PL is ill-conditioned (multiple compositions produce same transition).",
    "secondary": "oscillator_strength_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.6,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Semiconductor Physics",
    "integration_axis": "energy",
    "noise_model": "gaussian",
    "primitives": [
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      "E.kp_Hamiltonian",
      "O.iter",
      "O.states_transitions"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "optical_spectroscopy_PL_absorption",
    "solution_space": "wavefunctions_energies_of_confined_states",
    "sub_domain": "Confined electronic states",
    "title": "Quantum Well and Quantum Dot Electronic Structure"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "kp_schrodinger_forward"
    ],
    "allowed_omega_dimensions": [
      "geometry",
      "size_nm",
      "composition_In",
      "strain_pct",
      "T_K",
      "basis_N"
    ],
    "allowed_problem_classes": [
      "qdot_electronic_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "E_1 error \u003c= 2 meV",
      "forward_operator": "kp_schrodinger_forward",
      "input_format": "measurement_only",
      "omega": {
        "T_K": 4,
        "basis_N": 8,
        "composition_In": 0.5,
        "geometry": "InGaAs_QD_on_GaAs",
        "size_nm": 20,
        "strain_pct": 7
      },
      "problem_class": "qdot_electronic_inversion"
    },
    "epsilon_bounds": {
      "energy_error_meV": [
        0.5,
        50.0
      ]
    },
    "omega_bounds": {
      "T_K": [
        4,
        300
      ],
      "basis_N": [
        4,
        20
      ],
      "composition_In": [
        0.05,
        1.0
      ],
      "size_nm": [
        2,
        100
      ],
      "strain_pct": [
        0,
        10
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Confined electronic states",
  "title": "Quantum Well and Quantum Dot Electronic Structure"
}

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