Update README.md

.gitignore

@@ -1,3 +1,9 @@
+# VSCode
+.vscode/
+
+# HPC scripts and logs
+hpc/
+
 # Calculation outputs
 *.dat
 *.csv

Hamiltonian.jl

@@ -68,8 +68,8 @@ end
 
 "cuTENSOR contraction and accumulation (C = A * B + C)"
 function contract_accumulate!(C::CuTensor, A::CuTensor, B::CuTensor)::CuTensor
-    CUTENSOR.contraction!(one(eltype(C)), A.data, A.inds, CUTENSOR.CUTENSOR_OP_IDENTITY, B.data, B.inds, CUTENSOR.CUTENSOR_OP_IDENTITY,
+    cuTENSOR.contraction!(one(eltype(C)), A.data, A.inds, cuTENSOR.CUTENSOR_OP_IDENTITY, B.data, B.inds, cuTENSOR.CUTENSOR_OP_IDENTITY,
-                          one(eltype(C)), C.data, C.inds, CUTENSOR.CUTENSOR_OP_IDENTITY, CUTENSOR.CUTENSOR_OP_IDENTITY)
+                          one(eltype(C)), C.data, C.inds, cuTENSOR.CUTENSOR_OP_IDENTITY, cuTENSOR.CUTENSOR_OP_IDENTITY)
     return C
 end
 

LocalPreferences.toml

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+[TensorOperations]
+precompile_workload = true

Project.toml

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+[deps]
+CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
+NVTX = "5da4648a-3479-48b8-97b9-01cb529c0a1f"
+Preferences = "21216c6a-2e73-6563-6e65-726566657250"
+TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
+cuTENSOR = "011b41b2-24ef-40a8-b3eb-fa098493e9e1"

README.md

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+# DVR-jl
+
+Solves the quantum $n$-body problem in finite volume (lattice) with periodic boundary conditions. Uses discrete variable representation (DVR) with optional support for complex scaling to study resonances. All details can be found in [H. Yu, N. Yapa, and S. König, Complex scaling in finite volume, Phys. Rev. C 109, 014316 (2024)](https://doi.org/10.1103/PhysRevC.109.014316).
+
+Written in Julia with optional CUDA GPU acceleration (experimental).
+
+## Installation
+
+Make sure you have Julia installed. Required packages can be installed with a single command:
+```bash
+julia --project=. -e 'import Pkg; Pkg.instantiate()'
+```
+
+## Usage
+
+See `calculations/3b_bound.jl` for an example on a 3-body bound state.
+See `calculations/3b_res_from_paper.jl` for an example of a 3-body resonance via complex scaling.
+
+## Planned features
+
+- [ ] Spin and isospin degrees of freedom for nuclear calculations
+- [ ] Multi-node HPC support
+- [ ] Parity and cubic symmetries ($S_4$)
+
+## Acknowledgments
+
+The author gratefully acknowledges the guidance from Sebastian König.

calculations/3b_bound.jl

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+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32
+
+V_gauss(r2) = -2 * exp(-r2 / 4)
+
+d = 3
+n = 3
+N = 20
+L = 15
+n_imag = 1
+ϕ = 0
+
+s = system{T}(d, n, N, L)
+H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+@time evals, _, info = eig(H, 5)
+
+print(info.numops, " operations")
+display(evals)

calculations/3b_res_from_paper.jl

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+# 10.1007/s00601-020-01550-8
+# Fig. 7
+# E_R = 4.18(8)
+
+#./En.run -d 3 -n 3 -N 16 -c pot=v_shifted_gauss,v0=2.0,r=1.5,a=3.0 -c n_eig=20 -c which=li -c tol=1e-6 -L 16 -c phi=0.3 -v
+
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+using Plots
+
+V_gauss(r2) =
+    2 * exp(-((sqrt(r2) - 3) / 1.5) ^ 2)
+
+d = 3
+n = 3
+N = 16
+L = 16
+n_imag = 0
+
+for ϕ::T in 0.2:0.05:0.4
+    s = system{T}(d, n, N, L)
+    H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+    @time evals, _, info = eig(H, 20)
+    
+    print(info.numops, " operations")
+    display(evals)
+
+    scatter(real.(evals), imag.(evals); legend=false)
+    xlabel!("Re E")
+    ylabel!("Im E")
+    xlims!(0, 6)
+    ylims!(-0.6, 0)
+    savefig("temp/phi$(Int(round(ϕ * 100))).png")
+end

calculations/ComplexScaling-FV-P-res.jl

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+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_gauss(r2) =
+    -10 * exp(-(sqrt(r2)) ^ 2)
+
+d = 3
+n = 2
+N = 96
+ϕ = pi/6
+n_imag = 1
+
+open("ComplexScaling-FV-P-res.dat", "w") do f
+    for L = range(20, 35, length=16)
+        println("Calculating L=", L)
+        s = system{T}(d, n, N, L)
+        H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+        @time evals, _, info = eig(H, 40)
+
+        dataline = vcat([L], hcat(real.(evals), imag.(evals))'[:])
+        println(f, join(dataline, '\t'))
+    end
+end

calculations/ComplexScaling-FV-S-bound-phi.jl

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+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_gauss(r2) =
+    -10 * exp(-(sqrt(r2)) ^ 2)
+
+d = 3
+n = 2
+N = 30
+L = 6
+n_imag = 1
+
+open("ComplexScaling-FV-S-bound-phi.dat", "w") do f
+    for ϕ = range(0.0, 0.5, length=11)
+        println("Calculating ϕ=", ϕ)
+        s = system{T}(d, n, N, L)
+        H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+        @time evals, _, info = eig(H, 10, resonances = false)
+
+        dataline = vcat([ϕ], hcat(real.(evals), imag.(evals))'[:])
+        println(f, join(dataline, '\t'))
+    end
+end

calculations/ComplexScaling-FV-S-res-phi.jl

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+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_gauss(r2) =
+    2 * exp(- ((sqrt(r2)-3)/1.5) ^ 2)
+
+d = 3
+n = 2
+N = 96
+L = 30
+n_imag = 1
+
+open("ComplexScaling-FV-S-res-phi.dat", "w") do f
+    for ϕ = range(0.1, 0.6, length=26)
+        println("Calculating ϕ=", ϕ)
+        s = system{T}(d, n, N, L)
+        H = Hamiltonian{T}(s, V_gauss, ϕ, n_imag, mode)
+        @time evals, _, info = eig(H, 40, resonances = true)
+
+        dataline = vcat([ϕ], hcat(real.(evals), imag.(evals))'[:])
+        println(f, join(dataline, '\t'))
+    end
+end

calculations/EC-R2R-S.jl

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+using Plots, Arpack
+
+include("../helper.jl")
+include("../Hamiltonian.jl")
+
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_r2(c) = r2 -> c * (-5 * exp(-r2/3) + 2 * exp(-r2/10))
+
+d = 3
+n = 2
+N = 48
+L = 30
+ϕ = pi/6
+n_imag = 1
+s = system{T}(d, n, N, L)
+
+train_cs = range(0.78, 0.45, length=5)
+train_ref = reverse([0.05387926313545913-0.008900278182520881im,
+    0.11254295298924327-0.020515067379548786im,
+    0.16060154707503538-0.03716539208626717im,
+    0.19741353362674618-0.05994519982799412im,
+    0.2219100763497223-0.08959449893439568im])
+
+extrapolate_cs = range(0.38, 0.22, length=5)
+extrapolate_ref = reverse([0.23165109150003316-0.12052751440975719im,
+    0.23190549514995962-0.1406687118589838im,
+    0.22763660218046278-0.1626190970863793im,
+    0.21807104244164865-0.18635600686249373im,
+    0.2020979906072586-0.21180157628258728im])
+
+training_E = ComplexF64[]
+training_vec = Array[]
+exact_E = ComplexF64[]
+extrapolated_E = ComplexF64[]
+
+for c in train_cs
+    println("Training c=", c)
+    H = Hamiltonian{T}(s, V_r2(c), ϕ, n_imag, mode)
+    @time evals, evecs, info = eig(H, 20, resonances = true)
+    i = nearestIndex(evals, pop!(train_ref))
+    push!(training_E, evals[i])
+    push!(training_vec, evecs[i])
+end
+
+N_EC = [sum(x .* y) for (x, y) in Iterators.product(training_vec, training_vec)]
+
+for c in extrapolate_cs
+    println("Extrapolating c=", c)
+    H = Hamiltonian{T}(s, V_r2(c), ϕ, n_imag, mode)
+    @time evals, _, info = eig(H, 40, resonances = true)
+    nearestE = nearest(evals, pop!(extrapolate_ref))
+    push!(exact_E, nearestE)
+    
+    # EC extrapolation
+    H_training_vec = H.(training_vec)
+    H_EC = [sum(x .* y) for (x, y) in Iterators.product(training_vec, H_training_vec)]
+
+    evals = eigvals(H_EC, N_EC)
+    push!(extrapolated_E, nearestE)
+end
+
+scatter(real.(training_E), imag.(training_E), label="training")
+scatter!(real.(exact_E), imag.(exact_E), label="exact")
+scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="extrapolated")
+savefig("temp/EC-R2R-S.pdf")

helper.jl

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+"Index of the nearest value in a list to a given reference point"
+nearestIndex(list::Array, ref) = argmin(norm.(list .- ref))
+
+"Nearest value in a list to a given reference point"
+nearest(list::Array, ref) = list[nearestIndex(list, ref)]