  We study the dynamics of a system comprising a single qubit interacting
equally with $N$ qubits (a "spin star" system). Although this model can be
solved exactly, the exact solution does not give much intuition for the
dynamics of the model. Here, we find an approximation that gives some insight
into the dynamics for a particular class of initial spin coherent states of the
$N$ qubits. We find an effective Hamiltonian for the system that is a finite
Kerr (one-axis twisting) Hamiltonian for the $N+1$ qubits. The initial spin
coherent state evolves to spin squeezed states on short timescales, and to
"multiple-cat" states (superpositions of many spin coherent states) on longer
timescales, a manifestation of the phenomenon of fractional revivals of the
initial state. The evolution of the system is visualised with phase space plots
($Q$-functions) that, when plotted against time, reveal a "quantum carpet"
pattern. Of particular interest is the fact that our approximation captures the
qualitative features of the model even for small values of $N$. This suggests
the possibility of observing the phenomenon of fractional revival in this model
for systems of few qubits.
