  In Advances in Mathematical Physics (2011) we showed that the weighted shift
$z^{p}\frac{d^{p+1}}{dz^{p+1}}$ $(p=0, 1, 2, ...)$ acting on classical Bargmann
space $\mathbb{B}_{p}$ is chaotic operator. In Journal of Mathematical physics
(2014), we constructed an chaotic weighted shift
$\mathbb{M}^{*^{p}}\mathbb{M}^{p+1}$ $(p=0, 1, 2, ...)$ on some lattice
Fock-Bargmann $\mathbb{E}_{p}^{\alpha}$ generated by the orthonormal basis
$e_{m}^{(\alpha,p)}(z) = e_{m}^{\alpha} ; m=p, p+1, ...$ where
$e_{m}^{\alpha}(z) =
(\frac{2\nu}{\pi})^{1/4}e^{\frac{\nu}{2}z^{2}}e^{-\frac{\pi^{2}}{\nu}(m
+\alpha)^{2} +2i\pi(m +\alpha)z}; m \in \mathbb{N}$ with $\nu, \alpha$ are real
numbers; $\nu > 0$, $\mathbb{M}$ is an weighted shift and $\mathbb{M^{*}}$ is
the adjoint of the $\mathbb{M}$. In this paper we study the chaoticity of
tensor product $\mathbb{M}^{*^{p}}\mathbb{M}^{p+1}\otimes
z^{p}\frac{d^{p}}{dz^{p+1}}$ $(p=0, 1, 2, ...)$ acting on
$\mathbb{E}_{p}^{\alpha}\otimes \mathbb{B}_{p}$.
