50 lines
1.5 KiB
Julia
50 lines
1.5 KiB
Julia
using Plots
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include("../helper.jl")
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include("../p_space.jl")
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# contour
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vertices = [0, 0.4 - 0.15im, 0.8, 6]
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subdivisions = [128, 128, 128]
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p, w = get_mesh(vertices, subdivisions)
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mesh_E = p.*p ./ (2*0.5)
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# ResonanceEC: Eq. (20)
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V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
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training_points = range(0.75, 0.45, 5)
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training_E = Vector{ComplexF64}(undef, length(training_points))
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EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
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for (j, c) in enumerate(training_points)
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evals, evecs = eigen(get_H_matrix(V_system(c), p, w))
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i = identify_pole_i(p, evals)
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training_E[j] = evals[i]
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EC_basis[:, j] = evecs[:, i]
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end
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extrapolate_points = range(0.40, 0.25, 5)
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ref_E = 0.2 - 0.1im
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exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
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extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
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EC_basis = gram_schmidt!(EC_basis, w)
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EC_basis_w = EC_basis .* w
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for (j, c) in enumerate(extrapolate_points)
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exact_E[j] = quick_pole_E(V_system(c))
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H = get_H_matrix(V_system(c), p, w)
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H_EC = transpose(EC_basis_w) * H * EC_basis
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evals = eigvals(H_EC)
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i = argmin(abs.(evals .- ref_E))
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global ref_E = evals[i]
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extrapolate_E[j] = evals[i]
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end
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scatter(real.(training_E), imag.(training_E), label="training")
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scatter!(real.(exact_E), imag.(exact_E), label="exact")
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scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
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plot!(real.(mesh_E), imag.(mesh_E), label="contour")
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xlims!(0,1)
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