102 lines
3.0 KiB
Plaintext
102 lines
3.0 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"using Plots, LinearAlgebra\n",
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"include(\"p_space.jl\")\n",
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"\n",
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"g0(R, p, q) = (exp(-(1/4)*(p + q)^2*R^2)*(-1 + exp(p*q*R^2))*R)/(2*sqrt(π))\n",
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"g1(R, p, q) = (exp(-(1/4)*(p + q)^2*R^2)*(2 + p*q*R^2 + exp(p*q*R^2)*(-2 + p*q*R^2)))/(2*p*sqrt(π)*q*R)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"vertices = (0, 0.4 - 0.2im, 0.8, 2, 4, 6)\n",
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"subdivisions = 64\n",
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"p, w = get_mesh(vertices, subdivisions)\n",
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"mesh_E = p.*p ./ (2*0.5)\n",
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"\n",
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"# ResonanceEC: Eq. (20)\n",
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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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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"training_points = range(0.75, 0.45, 5)\n",
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"training_E = Vector{ComplexF64}(undef, length(training_points))\n",
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"EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))\n",
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"\n",
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"for (j, c) in enumerate(training_points)\n",
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" evals, evecs = eigen(get_H_matrix(V_system(c), p, w))\n",
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" i = identify_pole_i(p, evals)\n",
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" training_E[j] = evals[i]\n",
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" EC_basis[:, j] = evecs[:, i]\n",
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"end\n",
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"\n",
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"scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
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"plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
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"xlims!(0,1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"extrapolate_points = range(0.40, 0.20, 5)\n",
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"ref_E = 0.2 - 0.1im\n",
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"\n",
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"exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
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"extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
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"\n",
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"for (j, c) in enumerate(extrapolate_points)\n",
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" exact_E[j] = quick_pole_E(V_system(c))\n",
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"\n",
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" EC_basis_w = EC_basis .* w\n",
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" H = get_H_matrix(V_system(c), p, w)\n",
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" H_EC = transpose(EC_basis) * H * EC_basis\n",
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" N_EC = transpose(EC_basis) * EC_basis\n",
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" evals = eigvals(H_EC, N_EC)\n",
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" i = argmin(abs.(evals .- ref_E))\n",
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" ref_E = evals[i]\n",
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" extrapolate_E[j] = evals[i]\n",
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"end\n",
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"\n",
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"scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
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"scatter!(real.(exact_E), imag.(exact_E), label=\"exact\")\n",
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"scatter!(real.(extrapolate_E), imag.(extrapolate_E), label=\"extrapolated\")\n",
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"plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
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"xlims!(0,1)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.9.0",
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"language": "julia",
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"name": "julia-1.9"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.9.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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