diff --git a/berggren_3body_resonance.jl b/berggren_3body_resonance.jl new file mode 100644 index 0000000..0f7cbf4 --- /dev/null +++ b/berggren_3body_resonance.jl @@ -0,0 +1,77 @@ +using LinearAlgebra, SparseArrays, Arpack +include("helper.jl") +include("p_space.jl") +include("ho_basis.jl") + +println("No of threads = ", Threads.nthreads()) +atol = 10^-5 +maxevals = 10^5 +R_cutoff = 16 + +Λ = 0 +m = 1.0 +μ1 = m * 1/2 +μ2 = m * 2/3 + +target = 4.0766890719636875 - 0.012758927741074495im + +V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2) +V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff) + +vertices = [0, 2 - 0.2im, 3, 4] +subdivisions = [15, 10, 10] +ks, ws = get_mesh(vertices, subdivisions) + +jmax = 4 +tri((j1, j2)) = triangle_ineq(j1, j2, Λ) +js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax))) + +basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2)) +basis_size = length(js) * length(ks)^2 +@assert length(basis) == basis_size "Something wrong with the basis" +println("Basis size = $basis_size") + +# generate Berggren bases +berg_bases = Vector{Matrix{ComplexF64}}(undef, jmax + 1) +berg_Es = Vector{Vector{ComplexF64}}(undef, jmax + 1) +for j in 0:jmax + berg_E, berg_basis = eigen(get_H_matrix((k, kp) -> V_l(j, k, kp), ks, ws); permute=false, scale=false) + N_berg = diag(transpose(berg_basis .* ws) * berg_basis) + berg_basis = berg_basis ./ transpose(sqrt.(N_berg)) + berg_bases[1 + j] = berg_basis + berg_Es[1 + j] = berg_E +end +to_berg_basis(mat, j) = transpose(berg_bases[1 + j] .* ws) * mat * berg_bases[1 + j] + +@time "U_berggren" begin + U_blocks = [kron(berg_bases[1 + j1], berg_bases[1 + j2]) for (j1, j2) in js] + U = blockdiag(sparse.(U_blocks)...) +end + +@time "T" begin + T_blocks = [kron_sum(to_berg_basis(get_T_matrix(ks, μ1), j1), to_berg_basis(get_T_matrix(ks, μ2), j2)) for (j1, j2) in js] + T = blockdiag(sparse.(T_blocks)...) +end + +@time "V1" begin + V1_blocks = [kron(to_berg_basis(get_V_matrix((k, kp) -> V_l(j1, k, kp), ks, ws), j1), I(length(ks))) for (j1, _) in js] + V1 = blockdiag(sparse.(V1_blocks)...) +end + +E_max = 30 +μω_global = 0.5 +μ1ω1 = μω_global * 1/2 +μ2ω2 = μω_global * 2 + +@time "V2_HO" V2_HO = get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global) + +@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true) +@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true) + +@time "V2_p" V2_p = W_left * V2_HO * transpose(W_right) +@time "V2" V2 = transpose(U) * V2_p * U + +@time "H" H = T + V1 + V2 + +@time "Eigenvalues" evals, _ = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=false, check=1) +display(evals)