How do I make polynomial solutions evolve over time?

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Aisha Mohamed
Aisha Mohamed 2021-7-15
I have periodic system of zeros for 4th degree polynomial, and I use this relation to make all zeros evolve over timE
$ |f(t)> = exp(i t H)|f(0)> $ where H is:
\begin{align}
%\[
H=
\begin{bmatrix}
1& -1i& 0 & 0 & 0\\
1i & 1 & 0 & 0 & 0 \\
0 & 0 & 2.5 & 0 & 0 \\
0 & 0 & 0 & 2.5 & 0\\
0 & 0 & 0 & 0 & 2.5
\end{bmatrix}
%\]
\end{align}
and f0 = [0.2 + 0.0010i;0.1 + 0.0010i; 0.1 + 0.0020i;-0.3 + 0.001i;0.6 - 0.7i]; and t= 0:0.01:4*pi and I want to show the paths of zeros of this polynomial :
p=[0.2 + 0.0010i 0.2000 + 0.0020i 0.2449 + 0.0049i -0.6000 + 0.0020i 0.6 - 0.7i]; .
I used matlab to show this paths of all zeros of p but when t increases I got this figure where 3 zeros do not move and 1 zero move
How can me solve this problem please? I will appreciate any help?

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