1030 lines
278 KiB
Text
1030 lines
278 KiB
Text
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"10000"
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"using SpiDy\n",
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"using NPZ\n",
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"using DataFrames\n",
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"using CSV\n",
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"using ProgressMeter\n",
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"using Random\n",
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"using Statistics\n",
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"using LinearAlgebra\n",
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"using Plots\n",
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"\n",
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"########################\n",
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"########################\n",
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"\n",
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"Δt = .1\n",
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"N = 300\n",
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"tspan = (0., N*Δt)\n",
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"saveat = (0:1:N)*Δt\n",
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"α = 0.16\n",
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"ω0 = 1.4\n",
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"Γ = 0.5\n",
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"J = LorentzianSD(α, ω0, Γ) # coloring the noise\n",
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"matrix = AnisoCoupling([-sin(π/4) 0. 0. # coupling to the environment\n",
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" 0. 0. 0.\n",
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" cos(π/4) 0. 0.]);\n",
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"\n",
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"matrix = IsoCoupling(1)\n",
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"\n",
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"T = .01\n",
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"noise = ClassicalNoise(T);\n",
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"\n",
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"nspin = 1 # number of spins\n",
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"\n",
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"s0 = zeros(3*nspin)\n",
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"for i in 1:nspin\n",
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" ϵ = 0.1\n",
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" s0tmp = [ϵ*rand(), ϵ*rand(), -1]\n",
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" s0[1+(i-1)*3:3+(i-1)*3] = s0tmp./norm(s0tmp)\n",
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"end\n",
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"J0 = 1.\n",
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"JH = Nchain(nspin, J0)\n",
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"\n",
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"nruns = 10000"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "6e3cdf02-c243-4622-a52a-a6d7f987c68d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Starting...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:29\u001b[39m:38\u001b[39m\n"
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]
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}
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],
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"source": [
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"println(\"Starting...\")\n",
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"progress = Progress(nruns);\n",
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"\n",
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"sols = zeros(nruns, length(saveat), 3*nspin)\n",
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"\n",
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"Threads.@threads for i in 1:nruns\n",
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" bfields = [bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise)];\n",
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" sol = diffeqsolver(s0, tspan, J, bfields, matrix; JH=JH, saveat=saveat);\n",
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" sols[i, :, :] = transpose(sol[:, :])\n",
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" next!(progress)\n",
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"end\n",
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"\n",
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"solavg = mean(sols, dims=1)[1, :, :];\n",
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"solstd = std(sols, dims=1)[1, :, :];"
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]
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},
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{
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"id": "d16b97dd-b9f5-415c-b388-2b1f3344be45",
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},
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"execution_count": 3,
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"metadata": {},
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}
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],
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"source": [
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"plot(saveat, solavg[:, 1], ribbon=solstd[:, 1])"
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]
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},
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{
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"cell_type": "code",
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"id": "a06addc4-47b2-4467-8148-3e68f3eae702",
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"metadata": {},
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"outputs": [
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{
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"plot(saveat, solavg[:, 2], ribbon=solstd[:, 2])"
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]
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},
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{
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"cell_type": "code",
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"id": "bc1686fd-d86d-42b0-9d87-bcb911526d00",
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"metadata": {},
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"outputs": [
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{
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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||
"plot(saveat, solavg[:, 3], ribbon=solstd[:, 3])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "59ac92d9-6a78-402b-91ae-3f5fd22cc6ff",
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"metadata": {},
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"outputs": [],
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"source": [
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"projected = zeros(nruns, length(saveat), 2)\n",
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"\n",
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"normalized_avg = [normalize(vec(row)) for row in eachrow(solavg)]\n",
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||
"\n",
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||
"Threads.@threads for i in 1:length(saveat)\n",
|
||
" n = normalized_avg[i, :][1]\n",
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"\n",
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" u = normalize(cross(n, [0,0,1]))\n",
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" v = cross(u, n)\n",
|
||
"\n",
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||
" for j in 1:nruns\n",
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||
" b = sols[j, i, :]\n",
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||
" proj = dot(b, n) * n\n",
|
||
" b_ort = b - proj\n",
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"\n",
|
||
" projected[j, i, 1] = dot(u,b)\n",
|
||
" projected[j, i, 2] = dot(v,b)\n",
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" end\n",
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"end"
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]
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},
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{
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"execution_count": 16,
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"id": "03467eca-3f0c-4bd4-b3f7-5649b68780bc",
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"metadata": {},
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"outputs": [
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{
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"histogram(projected[:, 70, 2])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "f6df949c-15b2-447f-a264-8ef48ce1725e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"nth_moment (generic function with 1 method)"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"function nth_moment(data, N)\n",
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" return mean(data .^ N)\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "e4ad51fc-0dc7-4106-99e4-2b29e54b1930",
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"metadata": {},
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"outputs": [],
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"source": [
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"using HypothesisTests"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "e5b9609e-f467-4bd7-9b51-9a4c1f175738",
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"metadata": {},
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"outputs": [],
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"source": [
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"JB = zeros(N)\n",
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"for i in 10:N\n",
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" JB[i] = HypothesisTests.JarqueBeraTest(projected[:, i, 1]).JB\n",
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"end"
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]
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},
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{
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"execution_count": 12,
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"id": "3ad3f882-caa1-4dfc-b83c-3b57c214ecea",
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"metadata": {},
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"outputs": [
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]
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},
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||
"execution_count": 12,
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||
"metadata": {},
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||
"output_type": "execute_result"
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}
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],
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"source": [
|
||
"plot(10:N, JB[10:N])"
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]
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},
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{
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"cell_type": "code",
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||
"execution_count": 13,
|
||
"id": "bb3c6b84-5b21-4d79-b5bc-3345a8f2d893",
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"metadata": {},
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"outputs": [
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{
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||
"data": {
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||
"text/plain": [
|
||
"Jarque-Bera normality test\n",
|
||
"--------------------------\n",
|
||
"Population details:\n",
|
||
" parameter of interest: skewness and kurtosis\n",
|
||
" value under h_0: \"0 and 3\"\n",
|
||
" point estimate: \"0.024334226316224686 and 2.969023598052513\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: fail to reject h_0\n",
|
||
" one-sided p-value: 0.4999\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 10000\n",
|
||
" JB statistic: 1.38673\n"
|
||
]
|
||
},
|
||
"execution_count": 13,
|
||
"metadata": {},
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||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"HypothesisTests.JarqueBeraTest(projected[:, 197, 1])"
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||
]
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||
},
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||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "e331f6c7-fb4b-4f21-84d3-6a3f203a95b6",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"Jarque-Bera normality test\n",
|
||
"--------------------------\n",
|
||
"Population details:\n",
|
||
" parameter of interest: skewness and kurtosis\n",
|
||
" value under h_0: \"0 and 3\"\n",
|
||
" point estimate: \"0.019720125889005284 and 2.974701096764015\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: fail to reject h_0\n",
|
||
" one-sided p-value: 0.6329\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 10000\n",
|
||
" JB statistic: 0.91482\n"
|
||
]
|
||
},
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"HypothesisTests.JarqueBeraTest(projected[:, 200, 1])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "240660fb-d008-4dab-8bc1-aaf530885102",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "8150abab-cacc-4617-9d95-bebdc4c7cac8",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Julia 1.7.3",
|
||
"language": "julia",
|
||
"name": "julia-1.7"
|
||
},
|
||
"language_info": {
|
||
"file_extension": ".jl",
|
||
"mimetype": "application/julia",
|
||
"name": "julia",
|
||
"version": "1.7.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|