Read the equation
The function assigns this combination of coupling parameters directly to lambda_1. It does not extract the smallest eigenvalue of the constructed full 44-by-44 matrix in this method. It should therefore be shown as a declared estimate rather than an independently solved spectral endpoint.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| lambda_1 | Assigned lower spectral estimate |
| alpha | Ring coupling |
| kappa | Diagonal amplitude |
| gamma | Cross-block coefficient |
| gamma_0 | Cross-helix coefficient |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
double lambda_44; // Highest (bonding)
double spectral_width;
};
SpectralSummary spectral_summary() const {
SpectralSummary s;
// λ₁ = -4α - κ - γ - γ₀ (lowest, antibonding)
s.lambda_1 = -4.0 * params_.alpha - params_.kappa_intra -
params_.gamma - params_.gamma_0;
// λ₂₂ = 0 (zero mode, Goldstone)
s.lambda_22 = 0.0;
// λ₄₄ = κ + 1.2β₀ + γ + 2.618η (highest, bonding)
s.lambda_44 = params_.kappa_intra + 1.2 * params_.beta_0 +
params_.gamma + 2.618 * params_.eta;
Exact original notation
λ₁ = -4α - κ - γ - γ₀ (lowest, antibonding)