Rough Berggren 3-body calculation

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)