Smooth band transition between population and coherence relaxation times. More...

Data Types
type	nlo_band_transition_type

Functions/Subroutines
subroutine, public	nlo_band_transition_prepare (energies, width, rate1, rate2, relaxation)
	Prepare Γ_H(X)=γ₂X+(γ₁−γ₂)exp[−(ad_H/w)²]X, ad_H(X)=[H,X].
real(dp) function, public	nlo_band_transition_rate (relaxation, iband, jband)
	Return the central relaxation rate for one band pair.
subroutine, public	nlo_band_transition_correction (relaxation, hamiltonian, density, grade, correction)
	Sum relaxation corrections for one complete Cartesian Taylor grade.

Detailed Description

Smooth band transition between population and coherence relaxation times.

Function/Subroutine Documentation

subroutine, public nlo_t1_t2_band_transition::nlo_band_transition_prepare	(	real(dp), dimension(:), intent(in)	energies,
		real(dp), intent(in)	width,
		real(dp), intent(in)	rate1,
		real(dp), intent(in)	rate2,
		type(nlo_band_transition_type), intent(inout)	relaxation )

Prepare Γ_H(X)=γ₂X+(γ₁−γ₂)exp[−(ad_H/w)²]X, ad_H(X)=[H,X].

Parameters

energies	Band energies in Hartree
width	Energy scale of the smooth transition in Hartree
rate1	Population damping energy in Hartree
rate2	Coherence damping energy in Hartree
relaxation	Prepared band transition state

Note: Central rates use EXP exactly. Positive grades use Cauchy's formula on two horizontal contours and Gauss-Hermite integration. The contour shifts and factors are generated from the Hermite Jacobi matrix; no fitted or tabulated coefficients enter the relaxation model. Taylor derivatives follow analytically from the resolvent equation. Contour points share one workspace; lower grades are reconstructed once per requested grade from the already solved physical density.

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real(dp) function, public nlo_t1_t2_band_transition::nlo_band_transition_rate	(	type(nlo_band_transition_type), intent(in)	relaxation,
		integer, intent(in)	iband,
		integer, intent(in)	jband )

Return the central relaxation rate for one band pair.

Parameters

relaxation	Prepared band transition state
iband	First band index
jband	Second band index

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subroutine, public nlo_t1_t2_band_transition::nlo_band_transition_correction	(	type(nlo_band_transition_type), intent(in)	relaxation,
		complex(dp), dimension(:, :, :), intent(in)	hamiltonian,
		complex(dp), dimension(:, :, :), intent(in)	density,
		integer, intent(in)	grade,
		complex(dp), dimension(:, :, :), intent(out)	correction )

Sum relaxation corrections for one complete Cartesian Taylor grade.

Parameters

relaxation	Prepared band transition state
hamiltonian	Hamiltonian Taylor coefficients in the band basis
density	Physical Taylor coefficients; only lower grades are read
grade	Requested total Cartesian derivative order, between one and four
correction	Corrections of this grade in nlo_derivative_indices order

Note: For Y_l=(ad_H−w z_l)⁻¹ρ and R_l,α=−Σ_{0<β≤α}[H_β,Y_l,α−β], Y_l,α=(ρ_α+R_l,α)/(Δε−w z_l). Only grades below the requested grade are needed in R_l,α. Reconstruct them for one contour point, accumulate all corrections of the requested grade, then reuse the workspace. No band-sized array carries a contour-point dimension. At grade four, 20 lower-grade matrices replace 35 matrices for each of 96 points.

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