52 lines
1.5 KiB
Julia
52 lines
1.5 KiB
Julia
using FastGaussQuadrature
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# Gaussian potentials in momentum space
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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))
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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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function gausslegendre_shifted(a, b, n)
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scale = (b - a) / 2
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shift = (a + b) / 2
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p, w = gausslegendre(n)
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p = p .* scale .+ shift
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w = w .* scale
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return (p, w)
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end
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function get_mesh(vertices, subdivisions)
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p = Vector{ComplexF64}()
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w = Vector{ComplexF64}()
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for (a, b) in zip(vertices, vertices[2:end])
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p_new, w_new = gausslegendre_shifted(a, b, subdivisions)
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append!(p, p_new)
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append!(w, w_new)
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end
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return (p, w)
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end
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get_V_matrix(V_pq, p, w) = V_pq.(p, transpose(p)) .* transpose(w)
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get_K_matrix(p, μ) = collect(Diagonal(p.*p ./ (2*μ)))
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get_H_matrix(V_pq, p, w, μ=0.5) = get_K_matrix(p, μ) + get_V_matrix(V_pq, p, w)
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function identify_pole_i(p, evals, μ=0.5)
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mesh_Es = (p.*p) ./ (2*μ)
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current_i = 0
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current_min_ΔE = -1.0
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for i in eachindex(evals)
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min_ΔE = minimum(abs.(mesh_Es .- evals[i]))
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if min_ΔE > current_min_ΔE
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current_i = i
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current_min_ΔE = min_ΔE
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end
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end
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return current_i
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end
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function quick_pole_E(V_pq, μ=0.5; cs_angle=0.5, cutoff=8.0, meshpoints=256)
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p, w = get_mesh([0, cutoff * exp(-1im * cs_angle)], meshpoints)
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evals = eigvals(get_H_matrix(V_pq, p, w))
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return evals[identify_pole_i(p, evals)]
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end |