L1 ⚛ L1-491 ⊙ Testnet

Non-Equilibrium Green's Function (NEGF) Quantum Transport

Semiconductor Physics · Nanoscale quantum transport

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⬇ L1-491.md

# ⚛ L1 Principle — Non-Equilibrium Green's Function (NEGF) Quantum Transport **ID:** `L1-491` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Semiconductor Physics — *Nanoscale quantum transport* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** green functions complex matrix > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554141 --- ## 🧠 1. Introduction **Non-Equilibrium Green's Function (NEGF) Quantum Transport** is a **nonlinear inverse problem** whose unknown lives in **green functions complex matrix** space, within the **Nanoscale quantum transport** sub-domain of **Semiconductor Physics**. Measurements consist of electrons collected by an electron detector via a **quantum tunneling spectroscopy** sensing mechanism. The forward operator applies, in order: E · hamiltonian build operator; E · self energy operator; computes eigen-pairs of a linear operator; O · current LDOS operator. Observations are corrupted by additive Gaussian noise. Dyson equation is numerically well-posed in principle but conditioning deteriorates with device size; self-consistent Born (SCBA) loops add non-linear coupling. ## ⚙ 2. Forward Model Physical chain: **x** → E · hamiltonian build → E · self energy → O · current LDOS → **y** (detector). ``` y = `O.current_LDOS` `E.self_energy` `E.hamiltonian_build` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.hamiltonian_build` | E · hamiltonian build operator | | `E.self_energy` | E · self energy operator | | `O.current_LDOS` | O · current ldos 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 | Semiconductor Physics | | Sub domain | Nanoscale quantum transport | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | green_functions_complex_matrix | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 10 | | L dag | 4 | ## 📡 4. Measurement Model Dyson equation is numerically well-posed in principle but conditioning deteriorates with device size; self-consistent Born (SCBA) loops add non-linear coupling. | Metric | Value | |---|---| | Metric | IV_log_relative_error | | Secondary | LDOS_KL_divergence | ## 📏 5. Operating Range (Ω) **Center problem class:** `negf_inversion` · **Forward operator:** `negf_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 300 | | V bias | — | 0.5 | | N sites | — | 200 | | N energy | — | 500 | | Scba tol | — | 0.0001 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 4 – 400 | | V bias | — | 0.001 – 2.0 | | N sites | — | 20 – 5000 | | N energy | — | 50 – 5000 | | Scba tol | — | 1e-06 – 0.01 | ## 🎯 6. Tolerance (ε) **Center tolerance:** log10(I) error <= 0.04 | Metric | Range | |---|---| | Iv log relative error | 0.005 – 0.4 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **IV_log_relative_error**, with κ = `5000` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4783c3f1fe60427384e4c98c762ee9d7203c7a31e74ba3c8d963fad1c911fead` - **Chain tx hash:** `0xa956b1c693a701b2798fc9a1f72b05c007c92a9ad1437127cec6e3f35778567a` - **Chain block:** `41554141` --- ## File Mapping This bundle consists of: `L1-491.md`, `L1-491.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-491.md` | Source of truth — edit this | Human or LLM | | `L1-491.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 `L1-491`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-491.md).
Regenerate L1-491.json so every field matches the Markdown.
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📋 JSON metadata

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  "artifact_id": "L1-491",
  "chain_block": 41554141,
  "chain_hash": "0x4783c3f1fe60427384e4c98c762ee9d7203c7a31e74ba3c8d963fad1c911fead",
  "chain_tx_hash": "0xa956b1c693a701b2798fc9a1f72b05c007c92a9ad1437127cec6e3f35778567a",
  "domain": "Semiconductor Physics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 5000,
    "metric": "IV_log_relative_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "IV_log_relative_error",
    "regime": "Dyson equation is numerically well-posed in principle but conditioning deteriorates with device size; self-consistent Born (SCBA) loops add non-linear coupling.",
    "secondary": "LDOS_KL_divergence"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "electron",
    "difficulty_delta": 10,
    "domain": "Semiconductor Physics",
    "integration_axis": "energy",
    "noise_model": "gaussian",
    "primitives": [
      "E.hamiltonian_build",
      "E.self_energy",
      "E.eigensolve",
      "O.current_LDOS"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "quantum_tunneling_spectroscopy",
    "solution_space": "green_functions_complex_matrix",
    "sub_domain": "Nanoscale quantum transport",
    "title": "Non-Equilibrium Green\u0027s Function (NEGF) Quantum Transport"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "negf_forward"
    ],
    "allowed_omega_dimensions": [
      "N_sites",
      "N_energy",
      "V_bias",
      "T_K",
      "SCBA_tol"
    ],
    "allowed_problem_classes": [
      "negf_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "log10(I) error \u003c= 0.04",
      "forward_operator": "negf_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_energy": 500,
        "N_sites": 200,
        "SCBA_tol": 0.0001,
        "T_K": 300,
        "V_bias": 0.5
      },
      "problem_class": "negf_inversion"
    },
    "epsilon_bounds": {
      "IV_log_relative_error": [
        0.005,
        0.4
      ]
    },
    "omega_bounds": {
      "N_energy": [
        50,
        5000
      ],
      "N_sites": [
        20,
        5000
      ],
      "SCBA_tol": [
        1e-06,
        0.01
      ],
      "T_K": [
        4,
        400
      ],
      "V_bias": [
        0.001,
        2.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Nanoscale quantum transport",
  "title": "Non-Equilibrium Green\u0027s Function (NEGF) Quantum Transport"
}

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