42-EFT.WP.Heat.Decoherence v1.0 | Chapter 1: Introduction & Scope

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Chapter 1: Introduction & Scope

I. Objectives & Boundaries

• Objective: establish a unified pipeline from thermal-noise spectra → system–bath coupling → decoherence channels → metrology/estimation → engineering mitigations, providing reusable minimal statements and executable workflows.
• Boundaries: focus on thermally induced decoherence and heat-transport coupling for low/mid-temperature quantum & coherent devices (superconducting, semiconductor spin, NV, opto-mechanical, acoustic, and 2D resonators). Excludes non-thermal vacuum fluctuations and high-energy processes unrelated to heat.
• P10-1 (Scope Principle): any measurable decoherence rate/frequency drift/spectral feature is determined by a specified system–bath Hamiltonian H = H_S + H_B + H_{SB} together with the environmental spectral density J(ω), response function χ(ω), and temperature T; statistical conventions are fully specified by the data contract.

II. Core Questions & Typical Scales

• Decoherence metrics: T_1, T_2, Γ_1 = 1/T_1, Γ_φ; quality factor Q; phase-noise S_{φφ}(ω) and frequency-noise S_{ff}(ω).
• Thermal noise & FDT: classical limit S_VV = 4 k_B T R; quantum FDT S_{xx}(ω) = 2 coth(ħω/2k_B T) · Im χ_{xx}(ω).
• Environmental spectra: J(ω) = η ω (ω/ω_c)^{s-1} e^{-ω/ω_c} (Ohmic/Sub/Super); cutoff ω_c, shape params η, s.
• Heat transport & scales: diffusion ∂_t T = α ∇^2 T; non-Fourier τ_q ∂_t q + q = -κ ∇T; interface thermal resistance R_K; mean free path l_mfp.
• Frequency convention: unify ω = 2π f; explicitly declare single-/double-sided PSD in the dataset.
• S10-1 (Master relation)
  Γ(ω, T; θ) = ℱ[ J(ω; θ_env), χ(ω; θ_sys), n̄(ω,T), 𝒢(geom, κ, R_K), ... ],
  where θ aggregates material/geometry/coupling/temperature/boundaries, and n̄ is the Bose occupation.

III. Volume Structure & Anchor Map

1. Structure:
   • Ch.2 terminology/symbols/metrology baseline (units/PSD/FDT, S20-*);
   • Ch.3 thermal baths & carriers (phonon/electron/photon/magnon, S30-*);
   • Ch.4 open-quantum-system formalisms (Lindblad/Redfield/Influence Functional, S40-*, I40-*);
   • Ch.5 fluctuation–dissipation & spectral estimation (FDT/Johnson/1/f/TLS, S50-*, I50-*);
   • Ch.6 heat transport & non-equilibrium (Fourier/Cattaneo/BTE/Landauer, S60-*, I60-*);
   • Ch.7 platform-specific decoherence channels (SC/semiconductor/spin/optomech/acoustic, S70-*);
   • Ch.8 coherence engineering (shielding/filtering/cooling/phononic crystals, S80-*, I80-*);
   • Ch.9 metrology & inference (T1/T2/Ramsey/echo/noise thermometry, S90-*, I90-*);
   • Ch.10 robustness & mitigation (DD/QEC/feedback/thermal drift, S100-*);
   • Ch.11 simulation stack & synthetic data (Langevin/BTE/stochastic Liouville, S110-*, I110-*);
   • Ch.12 interfaces & bindings (S120-*, I12-*);
   • Ch.13 case library (SC/NV/QD/optomech/acoustic/2D, S130-*).
2. M10-1 (Reading & reuse guide)
   Select platform → lock conventions & dataset → estimate spectrum (Ch.5) → map Γ_1/Γ_φ via Ch.4/7 → propose engineering improvements (Ch.8) → form confidence regions (Ch.9) → validate via SBC (Ch.11).

IV. Cross-Volume Links (Fixed Style)

• EFT.WP.Core.Metrology v1.0: dimensions/units/uncertainty & coverage; EFT.WP.Core.Equations v1.1: path/measure and shared constant c_ref; companion whitepaper Energy Threads: medium effective index n_eff and tension T_fil appear here only as thermal/spectral parameters.
• If propagation/arrival time appears (cross-discipline reuse), choose one T_arr convention and record convention/delta_form/gamma(ell)/d_ell in the dataset.

V. Quality Gates (This Chapter)

• Q1 Convention consistency: single- vs double-sided PSD and ω/f choice must be consistent; any change is versioned.
• Q2 Units/dimensions: all expressions pass check_dim; unit columns for phase/frequency/power complete.
• Q3 Identifiability: Fisher conditioning for the key map J(ω) → {Γ_1, Γ_φ} is controlled; if cond(F) > κ_th, mark in the dataset and refer to Ch.10 mitigation strategies.
• Q4 Traceability: sources of η, s, ω_c, χ(ω) (measurement/fit/literature) are traceable in dataset references.

VI. Minimal Terms & Symbols (This Volume)

• Thermal: T (K), β = 1/(k_B T), κ (W·m⁻¹·K⁻¹), α (m²·s⁻¹), R_K (K·m²·W⁻¹).
• Spectral: S_xx(ω) (PSD), J(ω) (bath spectral density), χ(ω) (response), ω_c, η, s.
• Decoherence: T_1, T_2, Γ_1, Γ_φ, Q, n̄(ω,T); channel tags TLS/1f/Johnson/phonon/radiative.
• Constants: k_B, ħ, c_ref; optional c_med.

VII. Audience & Deliverables

• Audience: quantum-device R&D, metrology engineers, materials & thermal-design teams.
• Deliverables: minimal P/S/M/I anchors, dataset/pipeline/error-budget card templates, implementation interfaces, and reproducibility bundle specs.