  We study spectral form factor in periodically-kicked bosonic chains. We
consider a family of models where a Hamiltonian with the terms diagonal in the
Fock space basis, including random chemical potentials and pair-wise
interactions, is kicked periodically by another Hamiltonian with
nearest-neighbor hopping and pairing terms. We show that for intermediate-range
interactions, random phase approximation can be used to rewrite the spectral
form factor in terms of a bi-stochastic many-body process generated by an
effective bosonic Hamiltonian. In the particle-number conserving case, i.e.,
when pairing terms are absent, the effective Hamiltonian has a non-abelian
$SU(1,1)$ symmetry, resulting in universal quadratic scaling of the Thouless
time with the system size, irrespective of the particle number. This is a
consequence of degenerate symmetry multiplets of the subleading eigenvalue of
the effective Hamiltonian and is broken by the pairing terms. In the latter
case, we numerically find a nontrivial systematic system-size dependence of the
Thouless time, in contrast to a related recent study for kicked fermionic
chains.
