Created
July 8, 2015 15:00
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Lindblad Master Equation Integration
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immutable QuLindbladMasterEq{H<:QuBase.AbstractQuMatrix, V<:QuBase.AbstractQuArray} <: QuEquation | |
hamiltonian::H | |
collapse_ops::Vector{V} | |
QuLindbladMasterEq(hamiltonian, collapse_ops) = new(hamiltonian, collapse_ops) | |
end | |
QuLindbladMasterEq{H<:QuBase.AbstractQuMatrix, V<:QuBase.AbstractQuArray}(hamiltonian::H, collapse_ops::Vector{V}) = QuLindbladMasterEq{H,V}(hamiltonian, collapse_ops) | |
function lindblad_op(hamiltonian::QuBase.AbstractQuMatrix, collapse_ops::Vector) | |
nb = size(coeffs(hamiltonian), 1) | |
nlop = length(collapse_ops) | |
heff = zeros(typeof(im*one(eltype(hamiltonian))), size(coeffs(hamiltonian))) | |
for l=1:nlop | |
heff = heff + 0.5*coeffs(collapse_ops[l])'*coeffs(collapse_ops[l]) | |
end | |
SI = Array(Int,0) | |
SJ = Array(Int,0) | |
Lvals = Array(typeof(im*one(eltype(hamiltonian))),0) | |
for m=1:nb | |
for n=1:nb | |
for i=1:nb | |
for j=1:nb | |
sm = (n-1)*nb + m | |
sj = (j-1)*nb + i | |
lv = zero(Complex128) | |
for l=1:nlop | |
lv = lv + coeffs(collapse_ops[l])[m,i]*coeffs(collapse_ops[l]')[n,j] | |
end | |
if j==n | |
lv = lv - im*coeffs(hamiltonian)[m,i] - heff[m,i] | |
end | |
if i==m | |
lv = lv + im*coeffs(hamiltonian)[j,n] - heff[j,n] | |
end | |
if real(lv)!=0 || imag(lv)!=0 | |
push!(SI, sm) | |
push!(SJ, sj) | |
push!(Lvals, lv) | |
end | |
end | |
end | |
end | |
end | |
return QuBase.similar_type(hamiltonian)(sparse(SI, SJ, Lvals, nb*nb, nb*nb)) | |
end | |
QuPropagator{QPM<:QuPropagatorMethod, QM<:QuBase.AbstractQuMatrix}(eq::QuLindbladMasterEq, init_state::QM, tlist, method::QPM) = QuPropagator{QPM,QM,QuLindbladMasterEq}(eq, init_state, tlist, method) | |
QuPropagator{QPM<:QuPropagatorMethod, QM<:QuBase.AbstractQuMatrix, COT<:QuBase.AbstractQuArray}(param::QuBase.AbstractQuMatrix, collapse_ops::Vector{COT}, init_state::QM, tlist, method::QPM) = QuPropagator{QPM,QM,QuLindbladMasterEq}(QuLindbladMasterEq(param,collapse_ops), init_state, tlist, method) |
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