Normalized route against extended precision and classical formulas

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Reference
normalized route against extended precision and classical formulas
Kind
precision: the same mathematics in mpmath at 60–80 digits, written separately in src/pystratify/references.py and benchmarks/mp_reference.py: proves the numerics, not the formulation
Calculated
rates, Lamb shift
Agreement
1e-10
A dipole beside a 25 nm sphere of m = 0.05 + 3.5i at 600 nm: decay rates against the 40-digit series Chew's sums over 400 orders in mpmath at 40 digits against PyStratify's adaptive order and logarithmic amplitudes; the total rate climbs as d⁻³ at contact (quenching) while the radiative rate stays finite.
5010015020025030010⁻²10⁻¹11010²10³10⁴distance from the surface [nm]Γ / Γ₀
total, radial, PyStratify total, tangential, PyStratify radiative, radial, PyStratify radiative, tangential, PyStratify total, radial, 40 digits total, tangential, 40 digits radiative, radial, 40 digits radiative, tangential, 40 digits
Hover to read values.
  • largest relative difference over the four rates: 8.89×10⁻¹²
  • PyStratify the lines, the reference the circles

Run it yourself: sphere_emitter_checks.py · test_normalized.py · test_shift.py · figures.py · SPHERE_EMITTER_CHECKS.md on GitHub, PyStratify 97e52a9