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Appendix A: Symbol & Units Table (Incremental)
I. Notes & Dependency Anchors
This appendix lists only symbols and units newly introduced or specialized in this volume. Global symbols, rigorous definitions, and metrology conventions are in EFT.WP.Core.Terms v1.0 and EFT.WP.Core.Metrology v1.0. All formulas/symbols/definitions are in English; cross-volume citations use the fixed style “volume + version + anchor (P/S/M/I)”. Inline symbols are wrapped in backticks.
II. Writing & Metrology Conventions (Restated)
- Inline examples: psi(r,t), Delta(k), A, B, E, J, xi, lambda_L, kappa, T_fil, n_eff.
- Any expression with division/integrals/composite operators must include parentheses and explicitly declare path and measure: gamma(ell), d ell.
- Two equivalent arrival-time conventions (do not mix):
T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ); T_arr = ( ∫ ( n_eff / c_ref ) d ell ). - Name collisions (mandatory separation): use T_temp (temperature) vs. T_fil (tension); n (number density) vs. n_eff (effective refractive index).
- Dimension check: every expression must pass check_dim; tables must include SI unit columns.
III. Symbol Table (Incremental)
Symbol | Name | Definition/Use | SI Unit | Dimension | Notes/Anchors |
|---|---|---|---|---|---|
psi(r,t) | order parameter | GL/BCS order parameter; ` | psi | ^2 ~ n_s` | — (normalized) |
Delta(k,r,t) | gap function | pairing symmetry / anisotropy | J | M L^2 T^-2 | — |
A(r,t) | vector potential | EM potential | V·s·m⁻¹ | M L T^-2 I^-1 | Gauge declared per chapter |
B(r,t) | magnetic flux density | B = curl A | T | M T^-2 I^-1 | — |
E(r,t) | electric field | E = -∂A/∂t - grad phi | V·m⁻¹ | M L T^-3 I^-1 | — |
J(r,t) | current density | transport response | A·m⁻² | I L^-2 | — |
xi | coherence length | GL/London characteristic scale | m | L | Principal components xi_i |
lambda_L | London penetration depth | screening scale | m | L | Principal components lambda_{L,i} |
kappa | GL parameter | kappa = lambda_L / xi | — | — | Use kappa_i in anisotropic media |
kappa_ij | GL tensor coefficient | kinetic term weight | J·s²·m⁻²·kg⁻¹ (equiv.) | — | Equivalent to eff. mass tensor form |
T_c | critical temperature | SC transition temperature | K | Θ | — |
H_c1, H_c2 | lower/upper critical field | vortex entry / SC breakdown | A·m⁻¹ or T | — | Direction set by ê |
n_s | superfluid density | SC carrier density | m⁻³ | L^-3 | — |
rho_s | superfluid stiffness | phase stiffness | J·m⁻³ | M L^-1 T^-2 | — |
m* | effective mass | carrier effective mass | kg | M | — |
alpha, beta | GL coefficients | free-energy coefficients | per formula | — | Dimension via check_dim |
sigma(ω) | complex conductivity | sigma = sigma1 + i sigma2 | S·m⁻¹ | I^2 T^3 M^-1 L^-3 | Frequency-domain |
T_fil(r) | tension | EFT intrinsic tension | N | M L T^-2 | Maps to design variables |
grad T_fil | tension gradient | effective “force” source | N·m⁻¹ | M T^-2 | Orientation/anisotropy driver |
eta_ij | tension-induced anisotropy kernel | renormalizes kappa_ij | — | — | See Ch. 3/4 |
K_T, K_G | nonlocal kernels | convolution kernels for tension/gradient | m⁻³ etc. (model-dep.) | — | Thin-film/nonlocal regimes |
n_eff(ω,χ) | effective refractive index | path-/band-dependent | — | — | Arrival time & propagation |
c_ref | reference light speed | arrival-time reference | m·s⁻¹ | L T^-1 | 299 792 458 (exact) |
Phi0_ref | flux quantum | h/(2e) | Wb | M L^2 T^-2 I^-1 | Value from metrology set |
gamma(ell) | path parametrization | propagation/measurement path | — | — | Must be explicit |
d ell | line element | path integrals | m | L | Must be explicit |
T_arr(ω) | arrival time | one of two conventions | s | T | Record delta_form |
J^{(T)} | tension-coupled current term | additive term from grad T_fil | A·m⁻² | I L^-2 | See Ch. 4/7 |
S_v | single-vortex entropy | Hall/Nernst modeling | J·K⁻¹ | M L^2 T^-2 Θ^-1 | See Ch. 5 |
T_BKT | KTB transition temperature | 2D unbinding point | K | Θ | See Ch. 5/6/11 |
IV. Constants & Reference Values (Adopted in this Volume)
Symbol | Definition | Value/Status | Unit | Note |
|---|---|---|---|---|
c_ref | reference light speed | 299 792 458 (exact) | m·s⁻¹ | SI |
h | Planck constant | exact | J·s | SI |
e | elementary charge | exact | C | SI |
k_B | Boltzmann constant | exact | J·K⁻¹ | SI |
Phi0_ref | flux quantum | h/(2e) (derived) | Wb | From h,e |
mu0_ref | magnetic constant (reference) | set by metrology ref. | N·A⁻² | Project reference |
V. Typical Dimensional Checks & Conversions
- J = (sigma) * (E): [A·m⁻²] = [S·m⁻¹] * [V·m⁻¹] ✓
- kappa = lambda_L / xi: dimensionless ✓
- T_arr (both conventions): [s] = [m·s⁻¹]⁻¹ * ∫[—]*[m] = ∫[—]*[m·s⁻¹]⁻¹ * [m] ✓
- μ0_ref H_c2 ~ Φ0_ref / (2π ξ_⊥ ξ_∥): [N·A⁻²]*[A·m⁻¹] = [Wb]/[m²] (equivalent) ✓
VI. Notation & Conventions (Fixed in this Volume)
- Fourier convention (default): F(k) = ∫ f(r) exp(-i k·r) d^3r; inverse uses +i. Any change must be declared in each chapter’s Pre-sets.
- Gauge & coordinates: default Coulomb/London gauges; mappings between experimental and lattice coordinates are given in figure notes and dataset cards.
- Naming ban: do not use T to denote temperature/tension/arrival-time in the same context; use T_temp for temperature.
- Angles/directions: anisotropy direction vector ê; principal-axis rotation angles via φ_0 (vortex) and argmax markers for H_c2(θ) extrema.
VII. Dataset Card Fields (Units & Provenance — Mandatory)
units:
lambda_L: "m"
xi: "m"
H_c1: "A·m^-1"
H_c2: "A·m^-1" # or "T"
sigma1: "S·m^-1"
sigma2: "S·m^-1"
T_arr: "s"
d: "m"
constants:
c_ref: 299792458.0
contracts:
convention: "pulled_const|integrand"
delta_form: "c_ref^-1 * ∫ n_eff dℓ" # or "∫ (n_eff/c_ref) dℓ"
gamma: "piecewise: free|fixture|substrate|film|sample"
d_ell: "m"
references: ["Ch.6 W_coh","Ch.7 T_arr","Core.Metrology v1.0"]
VIII. Quality Gate (This Appendix)
- All newly introduced symbols are registered and conflict-checked against Core.Terms.
- Units are complete; key relations pass check_dim.
- Any T_arr usage explicitly records convention/delta_form/gamma(ell)/d ell.
- Units and constants in dataset examples match the metrology reference set.
- Collision pairs (T_temp/T_fil, n/n_eff) are not mixed in text or figures.
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
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