{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "15a8b1c9",
"metadata": {},
"outputs": [],
"source": [
"using QuantumAlgebra\n",
"using SymPy\n",
"\n",
"dispnormal(x) = display(\"text/latex\",\"\\$ $(latex(x)) \\\\quad\\\\to\\\\quad $(latex(normal_form(x))) \\$\")\n",
"acomm(A,B) = A*B + B*A;"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d3e6611f",
"metadata": {},
"outputs": [],
"source": [
"ξp = param(:ξ_p,'n')\n",
"ϕ = param(:ϕ,'r',:i);"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2b467fba",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/latex": [
"${{\\xi}_p^{*}}^{2} {{\\phi}_{2}}^{2} + 2{\\xi}_p^{*} {\\xi}_p {{\\phi}_{2}}^{2} + {{\\xi}_p}^{2} {{\\phi}_{2}}^{2} + {{\\phi}_{1}}^{2} + {{\\phi}_{2}}^{2} + 2{\\xi}_p^{*} {\\phi}_{1} {\\phi}_{2}{a}_{1}^\\dagger + 2{\\xi}_p {\\phi}_{1} {\\phi}_{2}{a}_{1}^\\dagger + 2{\\xi}_p^{*} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger + 2{\\xi}_p {{\\phi}_{2}}^{2}{a}_{2}^\\dagger + 2{\\xi}_p^{*} {\\phi}_{1} {\\phi}_{2}{a}_{1} + 2{\\xi}_p {\\phi}_{1} {\\phi}_{2}{a}_{1} + 2{\\xi}_p^{*} {{\\phi}_{2}}^{2}{a}_{2} + 2{\\xi}_p {{\\phi}_{2}}^{2}{a}_{2} + {{\\phi}_{1}}^{2}{{a}_{1}^\\dagger}^{2} + 2{\\phi}_{1} {\\phi}_{2}{a}_{1}^\\dagger {a}_{2}^\\dagger + 2{{\\phi}_{1}}^{2}{a}_{1}^\\dagger {a}_{1} + 2{\\phi}_{1} {\\phi}_{2}{a}_{1}^\\dagger {a}_{2} + {{\\phi}_{2}}^{2}{{a}_{2}^\\dagger}^{2} + 2{\\phi}_{1} {\\phi}_{2}{a}_{2}^\\dagger {a}_{1} + 2{{\\phi}_{2}}^{2}{a}_{2}^\\dagger {a}_{2} + {{\\phi}_{1}}^{2}{{a}_{1}}^{2} + 2{\\phi}_{1} {\\phi}_{2}{a}_{1} {a}_{2} + {{\\phi}_{2}}^{2}{{a}_{2}}^{2}$"
],
"text/plain": [
"ξ_p*² ϕ(2)² + 2 ξ_p* ξ_p ϕ(2)² + ξ_p² ϕ(2)² + ϕ(1)² + ϕ(2)² + 2 ξ_p* ϕ(1) ϕ(2) a†(1) + 2 ξ_p ϕ(1) ϕ(2) a†(1) + 2 ξ_p* ϕ(2)² a†(2) + 2 ξ_p ϕ(2)² a†(2) + 2 ξ_p* ϕ(1) ϕ(2) a(1) + 2 ξ_p ϕ(1) ϕ(2) a(1) + 2 ξ_p* ϕ(2)² a(2) + 2 ξ_p ϕ(2)² a(2) + ϕ(1)² a†(1)² + 2 ϕ(1) ϕ(2) a†(1) a†(2) + 2 ϕ(1)² a†(1) a(1) + 2 ϕ(1) ϕ(2) a†(1) a(2) + ϕ(2)² a†(2)² + 2 ϕ(1) ϕ(2) a†(2) a(1) + 2 ϕ(2)² a†(2) a(2) + ϕ(1)² a(1)² + 2 ϕ(1) ϕ(2) a(1) a(2) + ϕ(2)² a(2)²"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi2 = normal_form((param(:ϕ,:1)* (a(1) + a(1)') + param(:ϕ,:2)* (a(2) + a(2)' + ξp + ξp'))^2)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b1fb740b",
"metadata": {},
"outputs": [],
"source": [
"P = Vector{QuantumAlgebra.Param}[]\n",
"B = Vector{QuantumAlgebra.BaseOperator}[]\n",
"T = Vector{Int64}();\n",
"\n",
"###\n",
"for (s,t) in phi2.terms\n",
" if !isempty(s.bares)\n",
" check0 = adjoint(s.bares).v\n",
" check1 = reshape([v::QuantumAlgebra.BaseOperator for v in adjoint(s.bares.v)],length(s.bares.v),)\n",
" if check0 ∉ B && check1 ∉ B\n",
" push!(B,s.bares.v)\n",
" push!(P,s.params)\n",
" push!(T,t)\n",
" end\n",
" end\n",
"end\n",
"\n",
"###\n",
"BB = [QuantumAlgebra.BaseOpProduct(b) for b in unique(B)]\n",
"\n",
"Punique = [P[findall(x->x==b.v, B)] for b in BB]\n",
"PP = [[QuantumAlgebra.QuTerm(0, QuantumAlgebra.δ[], pint, QuantumAlgebra.ExpVal[], QuantumAlgebra.Corr[], QuantumAlgebra.BaseOpProduct()) for pint in pext] for pext in Punique]\n",
"\n",
"TT = [T[findall(x->x==b.v, B)] for b in BB];"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "14a0b581",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8-element Vector{QuantumAlgebra.BaseOpProduct}:\n",
" a†(1)²\n",
" a(2)²\n",
" a(2)\n",
" a†(2) a(1)\n",
" a(1) a(2)\n",
" a(1)\n",
" a†(1) a(1)\n",
" a†(2) a(2)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"BB"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "cb239da9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8-element Vector{Vector{QuantumAlgebra.QuTerm}}:\n",
" [ϕ(1)² ]\n",
" [ϕ(2)² ]\n",
" [ξ_p ϕ(2)² , ξ_p* ϕ(2)² ]\n",
" [ϕ(1) ϕ(2) ]\n",
" [ϕ(1) ϕ(2) ]\n",
" [ξ_p ϕ(1) ϕ(2) , ξ_p* ϕ(1) ϕ(2) ]\n",
" [ϕ(1)² ]\n",
" [ϕ(2)² ]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"PP"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "8053ca79",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8-element Vector{Vector{Int64}}:\n",
" [1]\n",
" [1]\n",
" [2, 2]\n",
" [2]\n",
" [2]\n",
" [2, 2]\n",
" [2]\n",
" [2]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TT"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a1c1650b",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 36,
"id": "2d1057d0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8-element Vector{QuExpr}:\n",
" ϕ(1)² \n",
" ϕ(2)² \n",
" 2 ξ_p* ϕ(2)² + 2 ξ_p ϕ(2)² \n",
" 2 ϕ(1) ϕ(2) \n",
" 2 ϕ(1) ϕ(2) \n",
" 2 ξ_p* ϕ(1) ϕ(2) + 2 ξ_p ϕ(1) ϕ(2) \n",
" 2 ϕ(1)² \n",
" 2 ϕ(2)² "
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"AA = Vector{QuantumAlgebra.QuExpr}()\n",
"for (pext,text) in zip(PP,TT)\n",
" A = QuExpr()\n",
" for (pint,tint) in zip(pext,text)\n",
" QuantumAlgebra._add_with_auto_order!(A,pint,tint)\n",
" end\n",
" push!(AA,A)\n",
"end\n",
"\n",
"AA"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "6b06e547",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8-element Vector{QuantumAlgebra.BaseOpProduct}:\n",
" a†(1)²\n",
" a(2)²\n",
" a(2)\n",
" a†(2) a(1)\n",
" a(1) a(2)\n",
" a(1)\n",
" a†(1) a(1)\n",
" a†(2) a(2)"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"BB"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "548188cb",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "3a09f9a4",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "4ebe9442",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "2b03d42f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "8349c245",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 38,
"id": "521aa480",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"${{\\xi}_p^{*}}^{4} {{\\phi}_{2}}^{4} + 4{{\\xi}_p^{*}}^{3} {\\xi}_p {{\\phi}_{2}}^{4} + 6{{\\xi}_p^{*}}^{2} {{\\xi}_p}^{2} {{\\phi}_{2}}^{4} + 6{{\\xi}_p^{*}}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2} + 6{{\\xi}_p^{*}}^{2} {{\\phi}_{2}}^{4} + 4{\\xi}_p^{*} {{\\xi}_p}^{3} {{\\phi}_{2}}^{4} + 12{\\xi}_p^{*} {\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2} + 12{\\xi}_p^{*} {\\xi}_p {{\\phi}_{2}}^{4} + {{\\xi}_p}^{4} {{\\phi}_{2}}^{4} + 6{{\\xi}_p}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2} + 6{{\\xi}_p}^{2} {{\\phi}_{2}}^{4} + 3{{\\phi}_{1}}^{4} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2} + 3{{\\phi}_{2}}^{4} + 4{{\\xi}_p^{*}}^{3} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger + 12{{\\xi}_p^{*}}^{2} {\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger + 12{\\xi}_p^{*} {{\\xi}_p}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger + 12{\\xi}_p^{*} {{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger + 12{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger + 4{{\\xi}_p}^{3} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger + 12{\\xi}_p {{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger + 12{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger + 4{{\\xi}_p^{*}}^{3} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger + 12{{\\xi}_p^{*}}^{2} {\\xi}_p {{\\phi}_{2}}^{4}{a}_{2}^\\dagger + 12{\\xi}_p^{*} {{\\xi}_p}^{2} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger + 12{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger + 12{\\xi}_p^{*} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger + 4{{\\xi}_p}^{3} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger + 12{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger + 12{\\xi}_p {{\\phi}_{2}}^{4}{a}_{2}^\\dagger + 4{{\\xi}_p^{*}}^{3} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} + 12{{\\xi}_p^{*}}^{2} {\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} + 12{\\xi}_p^{*} {{\\xi}_p}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1} + 12{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} + 4{{\\xi}_p}^{3} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} + 12{\\xi}_p {{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1} + 12{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} + 4{{\\xi}_p^{*}}^{3} {{\\phi}_{2}}^{4}{a}_{2} + 12{{\\xi}_p^{*}}^{2} {\\xi}_p {{\\phi}_{2}}^{4}{a}_{2} + 12{\\xi}_p^{*} {{\\xi}_p}^{2} {{\\phi}_{2}}^{4}{a}_{2} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2} + 12{\\xi}_p^{*} {{\\phi}_{2}}^{4}{a}_{2} + 4{{\\xi}_p}^{3} {{\\phi}_{2}}^{4}{a}_{2} + 12{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2} + 12{\\xi}_p {{\\phi}_{2}}^{4}{a}_{2} + 6{{\\xi}_p^{*}}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} + 12{\\xi}_p^{*} {\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} + 6{{\\xi}_p}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} + 6{{\\phi}_{1}}^{4}{{a}_{1}^\\dagger}^{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} + 12{{\\xi}_p^{*}}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger + 24{\\xi}_p^{*} {\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger + 12{{\\xi}_p}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger {a}_{2}^\\dagger + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger + 12{{\\xi}_p^{*}}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} + 24{\\xi}_p^{*} {\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} + 12{{\\xi}_p}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} + 12{{\\phi}_{1}}^{4}{a}_{1}^\\dagger {a}_{1} + 12{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} + 12{{\\xi}_p^{*}}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2} + 24{\\xi}_p^{*} {\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2} + 12{{\\xi}_p}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger {a}_{2} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2} + 6{{\\xi}_p^{*}}^{2} {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} + 12{\\xi}_p^{*} {\\xi}_p {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} + 6{{\\xi}_p}^{2} {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{2}^\\dagger}^{2} + 6{{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} + 12{{\\xi}_p^{*}}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} + 24{\\xi}_p^{*} {\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} + 12{{\\xi}_p}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{2}^\\dagger {a}_{1} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} + 12{{\\xi}_p^{*}}^{2} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger {a}_{2} + 24{\\xi}_p^{*} {\\xi}_p {{\\phi}_{2}}^{4}{a}_{2}^\\dagger {a}_{2} + 12{{\\xi}_p}^{2} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger {a}_{2} + 12{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger {a}_{2} + 12{{\\phi}_{2}}^{4}{a}_{2}^\\dagger {a}_{2} + 6{{\\xi}_p^{*}}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} + 12{\\xi}_p^{*} {\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} + 6{{\\xi}_p}^{2} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} + 6{{\\phi}_{1}}^{4}{{a}_{1}}^{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} + 12{{\\xi}_p^{*}}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {a}_{2} + 24{\\xi}_p^{*} {\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {a}_{2} + 12{{\\xi}_p}^{2} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {a}_{2} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1} {a}_{2} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {a}_{2} + 6{{\\xi}_p^{*}}^{2} {{\\phi}_{2}}^{4}{{a}_{2}}^{2} + 12{\\xi}_p^{*} {\\xi}_p {{\\phi}_{2}}^{4}{{a}_{2}}^{2} + 6{{\\xi}_p}^{2} {{\\phi}_{2}}^{4}{{a}_{2}}^{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{2}}^{2} + 6{{\\phi}_{2}}^{4}{{a}_{2}}^{2} + 4{\\xi}_p^{*} {{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{3} + 4{\\xi}_p {{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{3} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {a}_{2}^\\dagger + 12{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {a}_{2}^\\dagger + 12{\\xi}_p^{*} {{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{2} {a}_{1} + 12{\\xi}_p {{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{2} {a}_{1} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {a}_{2} + 12{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {a}_{2} + 12{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}^\\dagger}^{2} + 12{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}^\\dagger}^{2} + 24{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{2}^\\dagger {a}_{1} + 24{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{2}^\\dagger {a}_{1} + 24{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger {a}_{2} + 24{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger {a}_{2} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger {{a}_{1}}^{2} + 12{\\xi}_p {{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger {{a}_{1}}^{2} + 24{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} {a}_{2} + 24{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} {a}_{2} + 12{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}}^{2} + 12{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}}^{2} + 4{\\xi}_p^{*} {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{3} + 4{\\xi}_p {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{3} + 12{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{{a}_{2}^\\dagger}^{2} {a}_{1} + 12{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{{a}_{2}^\\dagger}^{2} {a}_{1} + 12{\\xi}_p^{*} {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} {a}_{2} + 12{\\xi}_p {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} {a}_{2} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger {{a}_{1}}^{2} + 12{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger {{a}_{1}}^{2} + 24{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} {a}_{2} + 24{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} {a}_{2} + 12{\\xi}_p^{*} {{\\phi}_{2}}^{4}{a}_{2}^\\dagger {{a}_{2}}^{2} + 12{\\xi}_p {{\\phi}_{2}}^{4}{a}_{2}^\\dagger {{a}_{2}}^{2} + 4{\\xi}_p^{*} {{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}}^{3} + 4{\\xi}_p {{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}}^{3} + 12{\\xi}_p^{*} {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} {a}_{2} + 12{\\xi}_p {{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} {a}_{2} + 12{\\xi}_p^{*} {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {{a}_{2}}^{2} + 12{\\xi}_p {\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {{a}_{2}}^{2} + 4{\\xi}_p^{*} {{\\phi}_{2}}^{4}{{a}_{2}}^{3} + 4{\\xi}_p {{\\phi}_{2}}^{4}{{a}_{2}}^{3} + {{\\phi}_{1}}^{4}{{a}_{1}^\\dagger}^{4} + 4{{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{3} {a}_{2}^\\dagger + 4{{\\phi}_{1}}^{4}{{a}_{1}^\\dagger}^{3} {a}_{1} + 4{{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{3} {a}_{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {{a}_{2}^\\dagger}^{2} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{2} {a}_{2}^\\dagger {a}_{1} + 12{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {a}_{2}^\\dagger {a}_{2} + 6{{\\phi}_{1}}^{4}{{a}_{1}^\\dagger}^{2} {{a}_{1}}^{2} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}^\\dagger}^{2} {a}_{1} {a}_{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}^\\dagger}^{2} {{a}_{2}}^{2} + 4{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}^\\dagger}^{3} + 12{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {{a}_{2}^\\dagger}^{2} {a}_{1} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}^\\dagger}^{2} {a}_{2} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger {a}_{2}^\\dagger {{a}_{1}}^{2} + 24{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{2}^\\dagger {a}_{1} {a}_{2} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {a}_{2}^\\dagger {{a}_{2}}^{2} + 4{{\\phi}_{1}}^{4}{a}_{1}^\\dagger {{a}_{1}}^{3} + 12{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{1}^\\dagger {{a}_{1}}^{2} {a}_{2} + 12{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{1}^\\dagger {a}_{1} {{a}_{2}}^{2} + 4{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1}^\\dagger {{a}_{2}}^{3} + {{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{4} + 4{\\phi}_{1} {{\\phi}_{2}}^{3}{{a}_{2}^\\dagger}^{3} {a}_{1} + 4{{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{3} {a}_{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{2}^\\dagger}^{2} {{a}_{1}}^{2} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{{a}_{2}^\\dagger}^{2} {a}_{1} {a}_{2} + 6{{\\phi}_{2}}^{4}{{a}_{2}^\\dagger}^{2} {{a}_{2}}^{2} + 4{{\\phi}_{1}}^{3} {\\phi}_{2}{a}_{2}^\\dagger {{a}_{1}}^{3} + 12{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{a}_{2}^\\dagger {{a}_{1}}^{2} {a}_{2} + 12{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{2}^\\dagger {a}_{1} {{a}_{2}}^{2} + 4{{\\phi}_{2}}^{4}{a}_{2}^\\dagger {{a}_{2}}^{3} + {{\\phi}_{1}}^{4}{{a}_{1}}^{4} + 4{{\\phi}_{1}}^{3} {\\phi}_{2}{{a}_{1}}^{3} {a}_{2} + 6{{\\phi}_{1}}^{2} {{\\phi}_{2}}^{2}{{a}_{1}}^{2} {{a}_{2}}^{2} + 4{\\phi}_{1} {{\\phi}_{2}}^{3}{a}_{1} {{a}_{2}}^{3} + {{\\phi}_{2}}^{4}{{a}_{2}}^{4}$"
],
"text/plain": [
"ξ_p*⁴ ϕ(2)⁴ + 4 ξ_p*³ ξ_p ϕ(2)⁴ + 6 ξ_p*² ξ_p² ϕ(2)⁴ + 6 ξ_p*² ϕ(1)² ϕ(2)² + 6 ξ_p*² ϕ(2)⁴ + 4 ξ_p* ξ_p³ ϕ(2)⁴ + 12 ξ_p* ξ_p ϕ(1)² ϕ(2)² + 12 ξ_p* ξ_p ϕ(2)⁴ + ξ_p⁴ ϕ(2)⁴ + 6 ξ_p² ϕ(1)² ϕ(2)² + 6 ξ_p² ϕ(2)⁴ + 3 ϕ(1)⁴ + 6 ϕ(1)² ϕ(2)² + 3 ϕ(2)⁴ + 4 ξ_p*³ ϕ(1) ϕ(2)³ a†(1) + 12 ξ_p*² ξ_p ϕ(1) ϕ(2)³ a†(1) + 12 ξ_p* ξ_p² ϕ(1) ϕ(2)³ a†(1) + 12 ξ_p* ϕ(1)³ ϕ(2) a†(1) + 12 ξ_p* ϕ(1) ϕ(2)³ a†(1) + 4 ξ_p³ ϕ(1) ϕ(2)³ a†(1) + 12 ξ_p ϕ(1)³ ϕ(2) a†(1) + 12 ξ_p ϕ(1) ϕ(2)³ a†(1) + 4 ξ_p*³ ϕ(2)⁴ a†(2) + 12 ξ_p*² ξ_p ϕ(2)⁴ a†(2) + 12 ξ_p* ξ_p² ϕ(2)⁴ a†(2) + 12 ξ_p* ϕ(1)² ϕ(2)² a†(2) + 12 ξ_p* ϕ(2)⁴ a†(2) + 4 ξ_p³ ϕ(2)⁴ a†(2) + 12 ξ_p ϕ(1)² ϕ(2)² a†(2) + 12 ξ_p ϕ(2)⁴ a†(2) + 4 ξ_p*³ ϕ(1) ϕ(2)³ a(1) + 12 ξ_p*² ξ_p ϕ(1) ϕ(2)³ a(1) + 12 ξ_p* ξ_p² ϕ(1) ϕ(2)³ a(1) + 12 ξ_p* ϕ(1)³ ϕ(2) a(1) + 12 ξ_p* ϕ(1) ϕ(2)³ a(1) + 4 ξ_p³ ϕ(1) ϕ(2)³ a(1) + 12 ξ_p ϕ(1)³ ϕ(2) a(1) + 12 ξ_p ϕ(1) ϕ(2)³ a(1) + 4 ξ_p*³ ϕ(2)⁴ a(2) + 12 ξ_p*² ξ_p ϕ(2)⁴ a(2) + 12 ξ_p* ξ_p² ϕ(2)⁴ a(2) + 12 ξ_p* ϕ(1)² ϕ(2)² a(2) + 12 ξ_p* ϕ(2)⁴ a(2) + 4 ξ_p³ ϕ(2)⁴ a(2) + 12 ξ_p ϕ(1)² ϕ(2)² a(2) + 12 ξ_p ϕ(2)⁴ a(2) + 6 ξ_p*² ϕ(1)² ϕ(2)² a†(1)² + 12 ξ_p* ξ_p ϕ(1)² ϕ(2)² a†(1)² + 6 ξ_p² ϕ(1)² ϕ(2)² a†(1)² + 6 ϕ(1)⁴ a†(1)² + 6 ϕ(1)² ϕ(2)² a†(1)² + 12 ξ_p*² ϕ(1) ϕ(2)³ a†(1) a†(2) + 24 ξ_p* ξ_p ϕ(1) ϕ(2)³ a†(1) a†(2) + 12 ξ_p² ϕ(1) ϕ(2)³ a†(1) a†(2) + 12 ϕ(1)³ ϕ(2) a†(1) a†(2) + 12 ϕ(1) ϕ(2)³ a†(1) a†(2) + 12 ξ_p*² ϕ(1)² ϕ(2)² a†(1) a(1) + 24 ξ_p* ξ_p ϕ(1)² ϕ(2)² a†(1) a(1) + 12 ξ_p² ϕ(1)² ϕ(2)² a†(1) a(1) + 12 ϕ(1)⁴ a†(1) a(1) + 12 ϕ(1)² ϕ(2)² a†(1) a(1) + 12 ξ_p*² ϕ(1) ϕ(2)³ a†(1) a(2) + 24 ξ_p* ξ_p ϕ(1) ϕ(2)³ a†(1) a(2) + 12 ξ_p² ϕ(1) ϕ(2)³ a†(1) a(2) + 12 ϕ(1)³ ϕ(2) a†(1) a(2) + 12 ϕ(1) ϕ(2)³ a†(1) a(2) + 6 ξ_p*² ϕ(2)⁴ a†(2)² + 12 ξ_p* ξ_p ϕ(2)⁴ a†(2)² + 6 ξ_p² ϕ(2)⁴ a†(2)² + 6 ϕ(1)² ϕ(2)² a†(2)² + 6 ϕ(2)⁴ a†(2)² + 12 ξ_p*² ϕ(1) ϕ(2)³ a†(2) a(1) + 24 ξ_p* ξ_p ϕ(1) ϕ(2)³ a†(2) a(1) + 12 ξ_p² ϕ(1) ϕ(2)³ a†(2) a(1) + 12 ϕ(1)³ ϕ(2) a†(2) a(1) + 12 ϕ(1) ϕ(2)³ a†(2) a(1) + 12 ξ_p*² ϕ(2)⁴ a†(2) a(2) + 24 ξ_p* ξ_p ϕ(2)⁴ a†(2) a(2) + 12 ξ_p² ϕ(2)⁴ a†(2) a(2) + 12 ϕ(1)² ϕ(2)² a†(2) a(2) + 12 ϕ(2)⁴ a†(2) a(2) + 6 ξ_p*² ϕ(1)² ϕ(2)² a(1)² + 12 ξ_p* ξ_p ϕ(1)² ϕ(2)² a(1)² + 6 ξ_p² ϕ(1)² ϕ(2)² a(1)² + 6 ϕ(1)⁴ a(1)² + 6 ϕ(1)² ϕ(2)² a(1)² + 12 ξ_p*² ϕ(1) ϕ(2)³ a(1) a(2) + 24 ξ_p* ξ_p ϕ(1) ϕ(2)³ a(1) a(2) + 12 ξ_p² ϕ(1) ϕ(2)³ a(1) a(2) + 12 ϕ(1)³ ϕ(2) a(1) a(2) + 12 ϕ(1) ϕ(2)³ a(1) a(2) + 6 ξ_p*² ϕ(2)⁴ a(2)² + 12 ξ_p* ξ_p ϕ(2)⁴ a(2)² + 6 ξ_p² ϕ(2)⁴ a(2)² + 6 ϕ(1)² ϕ(2)² a(2)² + 6 ϕ(2)⁴ a(2)² + 4 ξ_p* ϕ(1)³ ϕ(2) a†(1)³ + 4 ξ_p ϕ(1)³ ϕ(2) a†(1)³ + 12 ξ_p* ϕ(1)² ϕ(2)² a†(1)² a†(2) + 12 ξ_p ϕ(1)² ϕ(2)² a†(1)² a†(2) + 12 ξ_p* ϕ(1)³ ϕ(2) a†(1)² a(1) + 12 ξ_p ϕ(1)³ ϕ(2) a†(1)² a(1) + 12 ξ_p* ϕ(1)² ϕ(2)² a†(1)² a(2) + 12 ξ_p ϕ(1)² ϕ(2)² a†(1)² a(2) + 12 ξ_p* ϕ(1) ϕ(2)³ a†(1) a†(2)² + 12 ξ_p ϕ(1) ϕ(2)³ a†(1) a†(2)² + 24 ξ_p* ϕ(1)² ϕ(2)² a†(1) a†(2) a(1) + 24 ξ_p ϕ(1)² ϕ(2)² a†(1) a†(2) a(1) + 24 ξ_p* ϕ(1) ϕ(2)³ a†(1) a†(2) a(2) + 24 ξ_p ϕ(1) ϕ(2)³ a†(1) a†(2) a(2) + 12 ξ_p* ϕ(1)³ ϕ(2) a†(1) a(1)² + 12 ξ_p ϕ(1)³ ϕ(2) a†(1) a(1)² + 24 ξ_p* ϕ(1)² ϕ(2)² a†(1) a(1) a(2) + 24 ξ_p ϕ(1)² ϕ(2)² a†(1) a(1) a(2) + 12 ξ_p* ϕ(1) ϕ(2)³ a†(1) a(2)² + 12 ξ_p ϕ(1) ϕ(2)³ a†(1) a(2)² + 4 ξ_p* ϕ(2)⁴ a†(2)³ + 4 ξ_p ϕ(2)⁴ a†(2)³ + 12 ξ_p* ϕ(1) ϕ(2)³ a†(2)² a(1) + 12 ξ_p ϕ(1) ϕ(2)³ a†(2)² a(1) + 12 ξ_p* ϕ(2)⁴ a†(2)² a(2) + 12 ξ_p ϕ(2)⁴ a†(2)² a(2) + 12 ξ_p* ϕ(1)² ϕ(2)² a†(2) a(1)² + 12 ξ_p ϕ(1)² ϕ(2)² a†(2) a(1)² + 24 ξ_p* ϕ(1) ϕ(2)³ a†(2) a(1) a(2) + 24 ξ_p ϕ(1) ϕ(2)³ a†(2) a(1) a(2) + 12 ξ_p* ϕ(2)⁴ a†(2) a(2)² + 12 ξ_p ϕ(2)⁴ a†(2) a(2)² + 4 ξ_p* ϕ(1)³ ϕ(2) a(1)³ + 4 ξ_p ϕ(1)³ ϕ(2) a(1)³ + 12 ξ_p* ϕ(1)² ϕ(2)² a(1)² a(2) + 12 ξ_p ϕ(1)² ϕ(2)² a(1)² a(2) + 12 ξ_p* ϕ(1) ϕ(2)³ a(1) a(2)² + 12 ξ_p ϕ(1) ϕ(2)³ a(1) a(2)² + 4 ξ_p* ϕ(2)⁴ a(2)³ + 4 ξ_p ϕ(2)⁴ a(2)³ + ϕ(1)⁴ a†(1)⁴ + 4 ϕ(1)³ ϕ(2) a†(1)³ a†(2) + 4 ϕ(1)⁴ a†(1)³ a(1) + 4 ϕ(1)³ ϕ(2) a†(1)³ a(2) + 6 ϕ(1)² ϕ(2)² a†(1)² a†(2)² + 12 ϕ(1)³ ϕ(2) a†(1)² a†(2) a(1) + 12 ϕ(1)² ϕ(2)² a†(1)² a†(2) a(2) + 6 ϕ(1)⁴ a†(1)² a(1)² + 12 ϕ(1)³ ϕ(2) a†(1)² a(1) a(2) + 6 ϕ(1)² ϕ(2)² a†(1)² a(2)² + 4 ϕ(1) ϕ(2)³ a†(1) a†(2)³ + 12 ϕ(1)² ϕ(2)² a†(1) a†(2)² a(1) + 12 ϕ(1) ϕ(2)³ a†(1) a†(2)² a(2) + 12 ϕ(1)³ ϕ(2) a†(1) a†(2) a(1)² + 24 ϕ(1)² ϕ(2)² a†(1) a†(2) a(1) a(2) + 12 ϕ(1) ϕ(2)³ a†(1) a†(2) a(2)² + 4 ϕ(1)⁴ a†(1) a(1)³ + 12 ϕ(1)³ ϕ(2) a†(1) a(1)² a(2) + 12 ϕ(1)² ϕ(2)² a†(1) a(1) a(2)² + 4 ϕ(1) ϕ(2)³ a†(1) a(2)³ + ϕ(2)⁴ a†(2)⁴ + 4 ϕ(1) ϕ(2)³ a†(2)³ a(1) + 4 ϕ(2)⁴ a†(2)³ a(2) + 6 ϕ(1)² ϕ(2)² a†(2)² a(1)² + 12 ϕ(1) ϕ(2)³ a†(2)² a(1) a(2) + 6 ϕ(2)⁴ a†(2)² a(2)² + 4 ϕ(1)³ ϕ(2) a†(2) a(1)³ + 12 ϕ(1)² ϕ(2)² a†(2) a(1)² a(2) + 12 ϕ(1) ϕ(2)³ a†(2) a(1) a(2)² + 4 ϕ(2)⁴ a†(2) a(2)³ + ϕ(1)⁴ a(1)⁴ + 4 ϕ(1)³ ϕ(2) a(1)³ a(2) + 6 ϕ(1)² ϕ(2)² a(1)² a(2)² + 4 ϕ(1) ϕ(2)³ a(1) a(2)³ + ϕ(2)⁴ a(2)⁴"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi4 = normal_form((param(:ϕ,:1)* (a(1) + a(1)') + param(:ϕ,:2)* (a(2) + a(2)' + ξp + ξp'))^4)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "aaf28bec",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"171"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi4.terms.count"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "515b72ab",
"metadata": {},
"outputs": [],
"source": [
"P = Vector{QuantumAlgebra.Param}[]\n",
"B = Vector{QuantumAlgebra.BaseOperator}[]\n",
"T = Vector{Int64}();\n",
"\n",
"###\n",
"for (s,t) in phi4.terms\n",
" if !isempty(s.bares)\n",
" check0 = adjoint(s.bares).v\n",
" check1 = reshape([v::QuantumAlgebra.BaseOperator for v in adjoint(s.bares.v)],length(s.bares.v),)\n",
" if check0 ∉ B && check1 ∉ B\n",
" push!(B,s.bares.v)\n",
" push!(P,s.params)\n",
" push!(T,t)\n",
" end\n",
" end\n",
"end\n",
"\n",
"###\n",
"BB = [QuantumAlgebra.BaseOpProduct(b) for b in unique(B)]\n",
"\n",
"Punique = [P[findall(x->x==b.v, B)] for b in BB]\n",
"PP = [[QuantumAlgebra.QuTerm(0, QuantumAlgebra.δ[], pint, QuantumAlgebra.ExpVal[], QuantumAlgebra.Corr[], QuantumAlgebra.BaseOpProduct()) for pint in pext] for pext in Punique]\n",
"\n",
"TT = [T[findall(x->x==b.v, B)] for b in BB];"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "f1cd1d2f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45-element Vector{QuantumAlgebra.BaseOpProduct}:\n",
" a†(2)² a(1)\n",
" a†(1) a†(2)³\n",
" a†(1)² a(1) a(2)\n",
" a†(2) a(2)\n",
" a†(1) a(1)²\n",
" a†(2) a(2)³\n",
" a†(2)³\n",
" a†(2) a(2)²\n",
" a†(2)³ a(1)\n",
" a(1) a(2)²\n",
" a†(1)³ a†(2)\n",
" a†(1)² a(2)\n",
" a†(1)² a(1)²\n",
" ⋮\n",
" a†(1) a†(2) a(2)²\n",
" a†(1)² a(2)²\n",
" a†(2)² a(2)²\n",
" a†(1) a†(2)² a(2)\n",
" a†(1) a(1)\n",
" a†(1) a†(2) a(2)\n",
" a†(2)² a(1) a(2)\n",
" a†(1) a†(2) a(1)²\n",
" a†(1)³\n",
" a†(1) a(1) a(2)\n",
" a†(1) a†(2)² a(1)\n",
" a†(1) a†(2) a(1)"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"BB"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "61c7aca9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45-element Vector{Vector{QuantumAlgebra.QuTerm}}:\n",
" [ξ_p ϕ(1) ϕ(2)³ , ξ_p* ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1)³ ϕ(2) ]\n",
" [ξ_p² ϕ(2)⁴ ]\n",
" [ξ_p ϕ(1)³ ϕ(2) , ξ_p* ϕ(1)³ ϕ(2) ]\n",
" [ϕ(2)⁴ ]\n",
" [ξ_p ϕ(2)⁴ , ξ_p* ϕ(2)⁴ ]\n",
" [ξ_p ϕ(2)⁴ , ξ_p* ϕ(2)⁴ ]\n",
" [ϕ(1) ϕ(2)³ ]\n",
" [ξ_p ϕ(1) ϕ(2)³ , ξ_p* ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1)³ ϕ(2) ]\n",
" [ξ_p ϕ(1)² ϕ(2)² , ξ_p* ϕ(1)² ϕ(2)² ]\n",
" [ϕ(1)⁴ ]\n",
" ⋮\n",
" [ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1)² ϕ(2)² ]\n",
" [ϕ(2)⁴ ]\n",
" [ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1)⁴ ]\n",
" [ξ_p ϕ(1) ϕ(2)³ , ξ_p* ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1) ϕ(2)³ ]\n",
" [ϕ(1)³ ϕ(2) ]\n",
" [ξ_p ϕ(1)³ ϕ(2) , ξ_p* ϕ(1)³ ϕ(2) ]\n",
" [ξ_p ϕ(1)² ϕ(2)² , ξ_p* ϕ(1)² ϕ(2)² ]\n",
" [ϕ(1)² ϕ(2)² ]\n",
" [ξ_p ϕ(1)² ϕ(2)² , ξ_p* ϕ(1)² ϕ(2)² ]"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"PP"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "8e61f757",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45-element Vector{Vector{Int64}}:\n",
" [12, 12]\n",
" [4]\n",
" [12]\n",
" [12]\n",
" [12, 12]\n",
" [4]\n",
" [4, 4]\n",
" [12, 12]\n",
" [4]\n",
" [12, 12]\n",
" [4]\n",
" [12, 12]\n",
" [6]\n",
" ⋮\n",
" [12]\n",
" [6]\n",
" [6]\n",
" [12]\n",
" [12]\n",
" [24, 24]\n",
" [12]\n",
" [12]\n",
" [4, 4]\n",
" [24, 24]\n",
" [12]\n",
" [24, 24]"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TT"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "4ca75419",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45-element Vector{QuExpr}:\n",
" 12 ξ_p* ϕ(1) ϕ(2)³ + 12 ξ_p ϕ(1) ϕ(2)³ \n",
" 4 ϕ(1) ϕ(2)³ \n",
" 12 ϕ(1)³ ϕ(2) \n",
" 12 ξ_p² ϕ(2)⁴ \n",
" 12 ξ_p* ϕ(1)³ ϕ(2) + 12 ξ_p ϕ(1)³ ϕ(2) \n",
" 4 ϕ(2)⁴ \n",
" 4 ξ_p* ϕ(2)⁴ + 4 ξ_p ϕ(2)⁴ \n",
" 12 ξ_p* ϕ(2)⁴ + 12 ξ_p ϕ(2)⁴ \n",
" 4 ϕ(1) ϕ(2)³ \n",
" 12 ξ_p* ϕ(1) ϕ(2)³ + 12 ξ_p ϕ(1) ϕ(2)³ \n",
" 4 ϕ(1)³ ϕ(2) \n",
" 12 ξ_p* ϕ(1)² ϕ(2)² + 12 ξ_p ϕ(1)² ϕ(2)² \n",
" 6 ϕ(1)⁴ \n",
" ⋮\n",
" 12 ϕ(1) ϕ(2)³ \n",
" 6 ϕ(1)² ϕ(2)² \n",
" 6 ϕ(2)⁴ \n",
" 12 ϕ(1) ϕ(2)³ \n",
" 12 ϕ(1)⁴ \n",
" 24 ξ_p* ϕ(1) ϕ(2)³ + 24 ξ_p ϕ(1) ϕ(2)³ \n",
" 12 ϕ(1) ϕ(2)³ \n",
" 12 ϕ(1)³ ϕ(2) \n",
" 4 ξ_p* ϕ(1)³ ϕ(2) + 4 ξ_p ϕ(1)³ ϕ(2) \n",
" 24 ξ_p* ϕ(1)² ϕ(2)² + 24 ξ_p ϕ(1)² ϕ(2)² \n",
" 12 ϕ(1)² ϕ(2)² \n",
" 24 ξ_p* ϕ(1)² ϕ(2)² + 24 ξ_p ϕ(1)² ϕ(2)² "
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"AA = Vector{QuantumAlgebra.QuExpr}()\n",
"for (pext,text) in zip(PP,TT)\n",
" A = QuExpr()\n",
" for (pint,tint) in zip(pext,text)\n",
" QuantumAlgebra._add_with_auto_order!(A,pint,tint)\n",
" end\n",
" push!(AA,A)\n",
"end\n",
"\n",
"AA"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "7fa98481",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45-element Vector{QuantumAlgebra.BaseOpProduct}:\n",
" a†(1)\n",
" a†(2)\n",
" a†(1)²\n",
" a†(1) a†(2)\n",
" a†(1) a(1)\n",
" a†(2) a(1)\n",
" a†(2) a(2)\n",
" a(2)²\n",
" a†(1)³\n",
" a†(1)² a†(2)\n",
" a†(1)² a(2)\n",
" a†(1) a†(2) a(1)\n",
" a†(1) a†(2) a(2)\n",
" ⋮\n",
" a†(1) a†(2) a(1) a(2)\n",
" a†(1) a†(2) a(2)²\n",
" a†(1) a(1)³\n",
" a†(1) a(1)² a(2)\n",
" a†(1) a(1) a(2)²\n",
" a†(2)⁴\n",
" a†(2)³ a(1)\n",
" a†(2)² a(1) a(2)\n",
" a†(2)² a(2)²\n",
" a†(2) a(1)² a(2)\n",
" a†(2) a(1) a(2)²\n",
" a†(2) a(2)³"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"perm = sortperm(BB)\n",
"BB[perm]"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "fddddcd6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45-element Vector{QuExpr}:\n",
" 4 ξ_p*³ ϕ(1) ϕ(2)³ + 12 ξ_p*² ξ_p ϕ(1) ϕ(2)³ + 12 ξ_p* ξ_p² ϕ(1) ϕ(2)³ + 12 ξ_p* ϕ(1)³ ϕ(2) + 12 ξ_p* ϕ(1) ϕ(2)³ + 4 ξ_p³ ϕ(1) ϕ(2)³ + 12 ξ_p ϕ(1)³ ϕ(2) + 12 ξ_p ϕ(1) ϕ(2)³ \n",
" 4 ξ_p*³ ϕ(2)⁴ + 12 ξ_p*² ξ_p ϕ(2)⁴ + 12 ξ_p* ξ_p² ϕ(2)⁴ + 12 ξ_p* ϕ(1)² ϕ(2)² + 12 ξ_p* ϕ(2)⁴ + 4 ξ_p³ ϕ(2)⁴ + 12 ξ_p ϕ(1)² ϕ(2)² + 12 ξ_p ϕ(2)⁴ \n",
" 6 ξ_p*² ϕ(1)² ϕ(2)² + 12 ξ_p* ξ_p ϕ(1)² ϕ(2)² + 6 ξ_p² ϕ(1)² ϕ(2)² + 6 ϕ(1)⁴ + 6 ϕ(1)² ϕ(2)² \n",
" 12 ξ_p*² ϕ(1) ϕ(2)³ + 24 ξ_p* ξ_p ϕ(1) ϕ(2)³ + 12 ξ_p² ϕ(1) ϕ(2)³ + 12 ϕ(1)³ ϕ(2) + 12 ϕ(1) ϕ(2)³ \n",
" 12 ϕ(1)⁴ \n",
" 12 ξ_p*² ϕ(1) ϕ(2)³ + 24 ξ_p* ξ_p ϕ(1) ϕ(2)³ + 12 ξ_p² ϕ(1) ϕ(2)³ + 12 ϕ(1)³ ϕ(2) + 12 ϕ(1) ϕ(2)³ \n",
" 12 ξ_p² ϕ(2)⁴ \n",
" 6 ξ_p*² ϕ(2)⁴ + 12 ξ_p* ξ_p ϕ(2)⁴ + 6 ξ_p² ϕ(2)⁴ + 6 ϕ(1)² ϕ(2)² + 6 ϕ(2)⁴ \n",
" 4 ξ_p* ϕ(1)³ ϕ(2) + 4 ξ_p ϕ(1)³ ϕ(2) \n",
" 12 ξ_p* ϕ(1)² ϕ(2)² + 12 ξ_p ϕ(1)² ϕ(2)² \n",
" 12 ξ_p* ϕ(1)² ϕ(2)² + 12 ξ_p ϕ(1)² ϕ(2)² \n",
" 24 ξ_p* ϕ(1)² ϕ(2)² + 24 ξ_p ϕ(1)² ϕ(2)² \n",
" 24 ξ_p* ϕ(1) ϕ(2)³ + 24 ξ_p ϕ(1) ϕ(2)³ \n",
" ⋮\n",
" 24 ϕ(1)² ϕ(2)² \n",
" 12 ϕ(1) ϕ(2)³ \n",
" 4 ϕ(1)⁴ \n",
" 12 ϕ(1)³ ϕ(2) \n",
" 12 ϕ(1)² ϕ(2)² \n",
" ϕ(2)⁴ \n",
" 4 ϕ(1) ϕ(2)³ \n",
" 12 ϕ(1) ϕ(2)³ \n",
" 6 ϕ(2)⁴ \n",
" 12 ϕ(1)² ϕ(2)² \n",
" 12 ϕ(1) ϕ(2)³ \n",
" 4 ϕ(2)⁴ "
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"AA[perm]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1e90eaa2",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.7.2",
"language": "julia",
"name": "julia-1.7"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.2"
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"nbformat": 4,
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