74 lines
1.8 KiB
Julia
74 lines
1.8 KiB
Julia
using Plots
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include("../EC.jl")
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include("../ho_basis.jl")
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include("../p_space.jl")
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function solve_E(H0, H1, c_vals, near_E)
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out_E = ComplexF64[]
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for c in c_vals
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println("Solving for c = $c")
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H = H0 + c .* H1
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evals, _ = eigs(H, sigma=near_E, maxiter=5000, ritzvec=false, check=1)
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new_E = nearest(evals, near_E)
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push!(out_E, new_E)
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end
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return out_E
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end
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# paramters of the system
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angle = 0.0 * pi
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μ = 0.5
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l = 0
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V1 = -5
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R1 = sqrt(3)
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V2 = 2
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R2 = sqrt(10)
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n_EC = 8
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train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC))
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near_E = 0.2 + 0.2im
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# HO basis
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HO_Es = zeros(ComplexF64, n_EC)
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begin
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println("HO basis calculation")
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μω_gen = 0.5 * exp(-1im * angle)
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n_max = 40
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ns = collect(0:n_max)
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ls = fill(l, n_max + 1)
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T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
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V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); μω_gen=μω_gen) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); μω_gen=μω_gen)
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HO_Es .= solve_E(T, V, train_cs, near_E)
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end
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# p-space
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p_space_Es = zeros(ComplexF64, n_EC)
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begin
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println("p-space calculation")
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vertices = [0, 4 * exp(-1im * angle)]
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subdivisions = [256]
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ks, ws = get_mesh(vertices, subdivisions)
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V_of_r(r) = V1 * exp(-r^2 / R1^2) + V2 * exp(-r^2 / R2^2)
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V_mat_elem(k, kp) = Vl_mat_elem(V_of_r, l, k, kp; atol=10^-5, maxevals=10^5, R_cutoff=16)
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V = get_V_matrix(V_mat_elem, ks, ws)
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T = get_T_matrix(ks, μ)
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p_space_Es .= solve_E(T, V, train_cs, near_E)
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end
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# Plotting
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scatter(real.(HO_Es), imag.(HO_Es), label="HO basis", marker=:circle, color=:blue)
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scatter!(real.(p_space_Es), imag.(p_space_Es), label="p-space", marker=:circle, color=:red)
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xlabel!("Re(E)")
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ylabel!("Im(E)")
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savefig("temp/p_space_vs_HO.pdf") |