Hi experts, I want to solve the Bloch equations numerically with one parameter. Thus I tried to use ParametricNDSolve, but this does not give me any result, even though there is no mistake. However, when I use NDSolve and just type in a value for the parameter, there is a solution. Therefor I suspect a mistake in my understanding of the ParametricNDSolve. My code looks like this:
\[Delta] = 0
\[Gamma] = 0.1
\[Omega] = 1
s = ParametricNDSolve[{Subscript[\[Rho], 22]'[
t] == -\[Gamma]*
Subscript[\[Rho], 22][
t] - (I/2*\[Omega]*Subscript[\[Rho], 21][t] -
I/2*Conjugate[\[Omega]]*Subscript[\[Rho], 12][t]),
Subscript[\[Rho], 11]'[
t] == \[Gamma]*
Subscript[\[Rho], 22][
t] + (I/2*\[Omega]*Subscript[\[Rho], 21][t] -
I/2*Conjugate[\[Omega]]*Subscript[\[Rho], 12][t]),
Subscript[\[Rho], 21]'[
t] == -(I*\[Delta] + g)*Subscript[\[Rho], 21][t] -
I/2*\[Omega]*(Subscript[\[Rho], 22][t] -
Subscript[\[Rho], 11][t]),
Subscript[\[Rho], 21]'[t] == Conjugate[Subscript[\[Rho], 12]'[t]],
Subscript[\[Rho], 11][0] == 1, Subscript[\[Rho], 22][0] == 0,
Subscript[\[Rho], 12][0] == 0,
Subscript[\[Rho], 21][0] == 0}, {Subscript[\[Rho], 11][t],
Subscript[\[Rho], 12][t], Subscript[\[Rho], 21][t],
Subscript[\[Rho], 22][t]}, {t, 0, 100}, {g}]
Plot[Evaluate[
Table[{Subscript[\[Rho], 22][g][t]} /. s, {g, 1, 2, 0.1}]], {t, 0,
100}, PlotRange -> All]
Does anyone see my mistake? Thanks, Emil