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Narrow-to-broad calculation

This commit is contained in:
Nuwan Yapa 2024-08-22 12:47:58 -04:00
parent bdc75a9a2b
commit 458030f73f
2 changed files with 64 additions and 3 deletions
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6
calculations/B2R_Berggren_poles.jl
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@ -52,12 +52,12 @@ for (j, c) in enumerate(extrapolate_points)
extrapolate_E[j] = evals[i] extrapolate_E[j] = evals[i]
end end
exportCSV("temp/2b_GSM.csv", (training_E, exact_E, extrapolate_E), ("training", "exact", "extrapolated")) exportCSV("temp/2b_GSM_B2R.csv", (training_E, exact_E, extrapolate_E), ("training", "exact", "extrapolated"))
scatter(real.(training_E), imag.(training_E), label="training") scatter(real.(training_E), imag.(training_E), label="training")
scatter!(real.(exact_E), imag.(exact_E), label="exact") scatter!(real.(exact_E), imag.(exact_E), label="exact")
scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated") scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
scatter!(real.(basis_E), imag.(basis_E), m=:x, label="Berggren basis") scatter!(real.(basis_E), imag.(basis_E), m=:x, label="Berggren basis")
xlims!(-0.3,0.3) xlims!(0,0.3)
ylims!(-0.120,0.020) ylims!(-0.120,0.020)
savefig("temp/2b_GSM.pdf") savefig("temp/2b_GSM_B2R.pdf")

61
calculations/R2R_Berggren_poles.jl Normal file
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@ -0,0 +1,61 @@
using Plots
include("../helper.jl")
include("../p_space.jl")
# contour
p, w = get_mesh([0, 0.4 - 0.08im, 0.8, 6], [128, 128, 128])
# ResonanceEC: Eq. (20)
V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
# generating a Berggren basis with a pole using the same system
basis_c = 0.6
basis_E, berg_basis = eigen(get_H_matrix(V_system(basis_c), p, w); permute=false, scale=false)
basis_p = sqrt.(basis_E)
N_berg = sqrt.(diag(transpose(berg_basis .* w) * berg_basis))
berg_basis = berg_basis ./ transpose(N_berg)
berg_basis_w = berg_basis .* w
training_points = range(0.78, 0.62, 5) # original: range(1.35, 0.9, 5)
training_E = Vector{ComplexF64}(undef, length(training_points))
EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
# training
for (j, c) in enumerate(training_points)
H = get_H_matrix(V_system(c), p, w)
H_berg = transpose(berg_basis_w) * H * berg_basis
evals, evecs = eigen(H_berg)
i = identify_pole_i(basis_p, evals)
training_E[j] = evals[i]
EC_basis[:, j] = evecs[:, i]
end
N_EC = transpose(EC_basis) * EC_basis
extrapolate_points = range(0.58, 0.40, 5) # original: range(0.75, 0.40, 8)
exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
# extrapolating
for (j, c) in enumerate(extrapolate_points)
exact_E[j] = quick_pole_E(V_system(c))
H = get_H_matrix(V_system(c), p, w)
H_berg = transpose(berg_basis_w) * H * berg_basis
H_EC = transpose(EC_basis) * H_berg * EC_basis
evals = eigvals(H_EC, N_EC)
i = argmin(abs.(evals .- exact_E[j]))
extrapolate_E[j] = evals[i]
end
exportCSV("temp/2b_GSM_R2R.csv", (training_E, exact_E, extrapolate_E), ("training", "exact", "extrapolated"))
scatter(real.(training_E), imag.(training_E), label="training")
scatter!(real.(exact_E), imag.(exact_E), label="exact")
scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
scatter!(real.(basis_E), imag.(basis_E), m=:x, label="Berggren basis")
xlims!(0,0.3)
ylims!(-0.120,0.020)
savefig("temp/2b_GSM_R2R.pdf")