Solving a system of differential equations whose one of the coefficients is imported data

Suppose we have a coupled system of differential equations:
begin{equation}
frac{db}{dt}=(- gamma_b -iomega_b)b-ifrac{g}{2}p;quad
frac{dp}{dt}=ifrac{g}{2}Delta N(t) b-(gamma_a+gamma_b+2iJ)p.
end{equation}
If $Delta N$ was fixed, the solution of the system would be like
begin{equation}
begin{pmatrix}
b(t)
p(t)
end{pmatrix}=begin{pmatrix}
a_{11}&a_{12}
a_{21}&a_{22}
end{pmatrix}begin{pmatrix}
b(0)
p(0)
end{pmatrix}
end{equation}
Using the following code, I have found a $2times 2$ matrix (called sol) whose entries are $a_{ij}$ in the above equation:

rb=630;wb=75*10^6;g=0.63;ra=2.6*10^6;rm=3.6*10^6;J=6.3*10^7;DeltaN=0.164*10^5;
m ={{-rb-I wb,-I g/2},{I g DeltaN/2,-(ra+rm+2 I J)}};
eigvec = Eigenvectors[m] // Transpose // Simplify;
eigval = Eigenvalues[m] // Simplify;
inv = Inverse[eigvec] // Simplify;
v1 = eigval[[1]]; v2 = eigval[[2]];
sol = eigvec.{{E^(v1 t), 0}, {0, E^(v2 t) }}.inv;

If we suppose that $p(0)=0$, then one can easily plot $|b(t)/b(0)|^2$: simply plot $a_{11}(t)$. But the problem is that $Delta N$ is not fixed. It is a $Ntimes 1$ matrix which I have obtained from another code written with Fortran and its type is data.txt. The elements of this file are calculated by assuming the time interval between each one is $0.001$. That is, for $t=0.001$ we have $Delta N_1$, for $t=0.002$ we have $Delta N_2$, etc. But the time intervals are not included in the txt file.

One way that comes to my mind is this: Assuming we know the analytical form of solfor a fixed $Delta N$, we set time, i.g., equal to $0.001$ and then substitute the first row of the txt file (I call it $Delta N_1$) into sol and find $a_{11}$. Then we raise time to $0.002$, substitute $Delta N_1$ into sol, find $a_{11}$, and repeat the procedure to the last row of the txt file.

Now the question is this: how can I import the txt file to the code and do the procedure that I explained above to get some data like ${{0.001,a11(0.001)},{0.002,a11(0.002)},….}$ where the first elements are time intervals and the second ones are $a_{ij}$ corresponding to that particular time?

I had asked a similar question here enter link description here, but in that problem I did not have an external file with txt format.

I could not upload my txt file, so I write the first 10 elements if necessary:

0.164E+05

0.655E+05

0.146E+06

0.258E+06

0.400E+06

0.572E+06

0.776E+06

0.101E+07

0.129E+07

0.159E+07