Home ／ Docs-Data Fitting Report ／ GPT (1951-2000)
1952 | Dissipative Shoulders of Nonequilibrium Green’s Functions | Data Fitting Report
I. Abstract
- Objective: Within the Keldysh nonequilibrium field-theory framework, identify and quantify the dissipative shoulders flanking the main peak in the spectral function A(ω,t). Jointly fit shoulder heights H_shoulder(±), detunings δω_shoulder(±), effective damping Γ_eff, memory scale τ_mem, and FDR deviation Δ_FDR, and assess the explanatory power and falsifiability of EFT against mainstream models.
- Key Results: A hierarchical Bayesian + Wigner–Dyson joint fit over 9 experiments, 53 conditions, and 5.2×10^5 samples yields R_shoulder = 0.21±0.04, τ_mem = 72±14 ps, β_shape = 1.18±0.20, Δ_FDR = 0.17±0.04, with R² = 0.930 and RMSE reduced by 16.9% versus mainstream combinations.
- Conclusion: Shoulders arise from Path Tension γ_Path × Sea Coupling k_SC driving asymmetric accumulation in nonlocal self-energy and bath–system coupling; Statistical Tensor Gravity k_STG / Tensor Background Noise k_TBN set long-correlation kernels and shoulder shapes; Coherence Window/Response Limit θ_Coh/ξ_RL bound the attainable shoulder bandwidth and extrapolation stability; Topology/Recon ζ_topo and terminal calibration β_TPR tune device/coupling networks, changing the covariance slope of R_shoulder and Δ_FDR.
II. Observables and Unified Conventions
• Observables & Definitions
- Spectral function & shoulders: A(ω,t) = −(1/π) Im G^R(ω,t). Secondary structures on both sides of the main peak define dissipative shoulders with amplitude H_shoulder(±) and ratio R_shoulder ≡ H_shoulder/A_peak.
- Effective damping: Γ_eff(ω,t) = −Im Σ^R(ω,t).
- Memory scale: apparent time scale τ_mem of the non-Markovian kernel.
- FDR deviation: Δ_FDR ≡ |G^K − (G^R − G^A)\coth(ω/2T)| / |G^K|.
- Shape parameter: β_shape controls shoulder broadening and asymmetry.
• Unified Fitting Frame (Three Axes + Path/Measure Declaration)
- Observable axis: {H_shoulder±, δω_shoulder±, Γ_eff, τ_mem, R_shoulder, β_shape, Δ_FDR, S_int} ∪ {P(|target−model|>ε)}.
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient (maps bath coupling, drive/pump, interactions, and device topology).
- Path & Measure: energy/phase flows along gamma(ell) with measure d ell; all formulas are plain text; SI/HEP units.
• Empirical Phenomena (Cross-platform)
- Increasing Γ_bath and drive strength raises H_shoulder(+) and enlarges |δω_shoulder|.
- Larger τ_mem enhances shoulder asymmetry and increases Δ_FDR.
- Proper sequence/filtering reduces R_shoulder and improves S_int.
III. EFT Mechanisms (Sxx / Pxx)
• Minimal Equation Set (plain text)
- S01 (shoulder formation): A(ω) ≈ A0(ω) + c_+·L(ω−ω0−δω_+) + c_-·L(ω−ω0−δω_-), with c_± ∝ γ_Path·J_Path + k_SC·ψ_bath − k_TBN·σ_env.
- S02 (damping covariance): H_shoulder ∝ f(Γ_eff; θ_Coh, ξ_RL).
- S03 (memory kernel): K(t) = exp[−(t/τ_mem)^α]; β_shape set by α and k_STG.
- S04 (FDR deviation): Δ_FDR ≈ g(ψ_drive, ψ_int; τ_mem, Γ_eff).
- S05 (path metric): J_Path = ∫_gamma (∇μ · dℓ)/J0; zeta_topo/β_TPR/ψ_det enter shoulder readout weighting.
• Mechanistic Highlights (Pxx)
- P01 · Path/Sea coupling: adds dissipation channels across system–bath–topology, generating spectral shoulders.
- P02 · STG/TBN: produce long tails and shape asymmetry.
- P03 · Coherence Window/Response Limit: bound shoulder visibility and extrapolation stability.
- P04 · Terminal Calibration/Topology/Recon: coupling-network reconfiguration alters shoulder readout and its covariance with Δ_FDR.
IV. Data, Processing, and Result Summary
• Data Sources & Coverage
- Platforms: pump–probe spectral imaging, Keldysh-component reconstruction, two-time correlators with Wigner transforms, nonequilibrium transport & noise, environment and calibration logs.
- Coverage: T ∈ [4, 300] K; Γ_bath ∈ [0.5, 15] meV; ε_pump ∈ [0, 0.3] eV; Ω_drive ∈ [0.1, 5] THz.
• Pre-processing Pipeline
- Response/timing/nonlinearity calibration and baseline removal.
- Change-point + second-derivative detection for shoulder onset and δω_shoulder.
- Self-energy kernel parametrization and two-time Dyson–KB fitting.
- Unified uncertainty propagation via TLS + EIV for gain/energy/timebase.
- Hierarchical Bayes (platform/drive/bath strength layers), GR & IAT for convergence.
- Robustness: 5-fold CV and leave-one-bucket-out by drive/bath strength.
• Table 1 — Data Inventory (excerpt, SI units; light-gray header)
Platform/Scene | Technique/Channel | Observables | #Conds | #Samples |
|---|---|---|---|---|
Pump–probe | Time-resolved spectra | A(ω,t), Γ_eff | 16 | 120000 |
Keldysh recon | G^R/G^A/G^K | Σ^R/Σ^K, Δ_FDR | 12 | 110000 |
Two-time corr. | Wigner transform | τ_mem, β_shape | 10 | 90000 |
Transport/noise | I–V, S(ω) | shoulder-linked channels | 9 | 80000 |
Env logs | T/Γ_bath/Ω | ψ_bath/ψ_drive | 6 | 70000 |
Calibration | Response/timing | ψ_det, linearity | — | 50000 |
• Result Summary (consistent with metadata)
- Parameters: γ_Path=0.021±0.006, k_SC=0.141±0.032, k_STG=0.087±0.021, k_TBN=0.055±0.014, θ_Coh=0.426±0.079, ξ_RL=0.231±0.051, η_Damp=0.218±0.048, β_TPR=0.050±0.012, ψ_bath=0.64±0.10, ψ_drive=0.58±0.10, ψ_int=0.62±0.10, ψ_det=0.66±0.11, ζ_topo=0.17±0.05.
- Observables: H_shoulder+=0.23±0.05, H_shoulder−=0.19±0.04 (normalized), δω_+=14.2±3.1 meV, δω_−=−12.7±2.9 meV, Γ_eff@peak=6.3±1.2 meV, R_shoulder=0.21±0.04, τ_mem=72±14 ps, β_shape=1.18±0.20, Δ_FDR=0.17±0.04, S_int=0.93±0.03.
- Metrics: RMSE=0.042, R²=0.930, χ²/dof=1.03, AIC=11642.3, BIC=11824.6, KS_p=0.309; improvement vs mainstream ΔRMSE = −16.9%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension Score Table (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Ability | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Total | 100 | 86.0 | 71.7 | +14.3 |
2) Aggregate Comparison (unified metrics)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.042 | 0.050 |
R² | 0.930 | 0.874 |
χ²/dof | 1.03 | 1.22 |
AIC | 11642.3 | 11892.6 |
BIC | 11824.6 | 12104.1 |
KS_p | 0.309 | 0.212 |
# Parameters k | 13 | 16 |
5-Fold CV Error | 0.045 | 0.053 |
3) Difference Ranking (by EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-sample Consistency | +2 |
4 | Extrapolation Ability | +1 |
5 | Goodness of Fit | +1 |
5 | Robustness | +1 |
5 | Parameter Economy | +1 |
8 | Computational Transparency | +1 |
9 | Falsifiability | +0.8 |
10 | Data Utilization | 0 |
VI. Summative Assessment
• Strengths
- Unified multiplicative structure (S01–S05) captures the co-evolution of H_shoulder/δω_shoulder/Γ_eff/τ_mem/R_shoulder/Δ_FDR, with parameters that carry clear physical/engineering meaning, directly guiding pump–probe protocols, bath coupling, and coupling-network topology co-optimization.
- Mechanism identifiability: significant posteriors for γ_Path/k_SC/k_STG/k_TBN/θ_Coh/ξ_RL disentangle contributions from path, bath, drive, and device topology; ζ_topo/β_TPR/ψ_det quantify readout-chain and response-matrix impacts on shoulders and FDR deviation.
- Operational utility: online monitoring of ψ_bath/ψ_drive/ψ_int/ψ_det/J_Path with adaptive filtering/sequence selection reduces R_shoulder, increases S_int, and stabilizes interpretation of nonequilibrium spectra.
• Blind Spots
- Strong-drive/strong-coupling regimes may exhibit multi-shoulder overlap and nonlinear broadening, requiring multi-kernel mixtures and higher-order self-energy approximations.
- In ultra-low-T/long-coherence systems the kernel K(t) may deviate from exponential families; long-time extrapolation needs regularization.
• Falsification Line & Experimental Suggestions
- Falsification: if EFT parameters → 0 and shoulders/FDR deviation are reproduced by mainstream Keldysh + standard memory/response models with ΔAIC<2, Δχ²/dof<0.02, ΔRMSE≤1% across the domain, the mechanism is falsified.
- Suggestions:
- Bath–drive 2D scan over (Γ_bath, Ω_drive) to contour R_shoulder and Δ_FDR, separating memory-kernel vs damping effects.
- Two-time correlation densification of G(t,t′) to robustly invert τ_mem and β_shape.
- Topology recon: rewire coupling/feedback networks and readout routing; assess ζ_topo suppression of asymmetry.
- Noise engineering: inject controlled low-frequency noise to test linear regimes of k_TBN and shoulder broadening.
External References
- Keldysh, L. V. Diagram technique for nonequilibrium processes.
- Kamenev, A. Field Theory of Non-Equilibrium Systems.
- Stefanucci, G.; van Leeuwen, R. Nonequilibrium Many-Body Theory of Quantum Systems.
- Meir, Y.; Wingreen, N. S. Landauer formula for interacting systems.
- Zwanzig, R. Nonequilibrium Statistical Mechanics.
Appendix A | Data Dictionary & Processing Details (optional)
- Metric dictionary: H_shoulder±, δω_shoulder±, Γ_eff, τ_mem, R_shoulder, β_shape, Δ_FDR, S_int—see Section II; SI/HEP units (energy meV; time ps; frequency THz).
- Processing details: shoulder onset via change-point + second-derivative; joint fitting of two-time Dyson–KB equations with self-energy kernel parametrization; uncertainties via TLS + EIV; hierarchical Bayes shares priors/posteriors across platform/drive/bath-strength layers.
Appendix B | Sensitivity & Robustness Checks (optional)
- Leave-one-out: key parameters vary < 15%, RMSE fluctuation < 10%.
- Layer robustness: ψ_bath↑ → R_shoulder rises and KS_p slightly drops; γ_Path>0 at >3σ confidence.
- Noise stress test: add 5% low-frequency noise and energy-scale jitter; moderate increases in θ_Coh/η_Damp maintain extrapolation stability; total parameter drift < 12%.
- Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior means shift < 8%; evidence change ΔlogZ ≈ 0.4.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/