Read the equation
The method assigns a linear combination of coupling parameters to lambda_44. This is separate from calculating the actual largest eigenvalue of the full matrix. The parameter coefficients are part of the project’s estimate and require validation before use as spectral bounds.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| lambda_44 | Assigned upper spectral estimate |
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
// 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;
// W = λ₄₄ - λ₁ = 4α + 2κ + 1.2β₀ + 2γ + γ₀ + 3.236η
s.spectral_width = s.lambda_44 - s.lambda_1;
return s;
}
// Approximate spectrum using block eigenvaluesExact original notation
λ₄₄ = κ + 1.2β₀ + γ + 2.618η (highest, bonding)