treated by the Schrödinger-Koopman approach. For this reason, at the starting point we consider a matrix model in a three dimensional space, the other compact six dimensions of the BFSS model emerging from the fluctuations in our approach. Note that the reduction to three dimensions, can also be interpreted as an orbifold reduction as in [@Berenstein].\
This paper is organized as follows. Section 2 presents elementary ingredients of the BFSS matrix theory. The different models used for the numerical simulations are also presented. Section 3 studies the dynamics of the quantum fluctuations, in particular we show the existence of an invariant torus in the phase space of the matrices modelizing the noncommutative D2-brane. Section 4 presents the main results of this paper concerning the dynamics of the fermionic string driven by the D2-brane: a quantum chaos signature in its spectrum, an horizon of coherence in the evolution of its reduced density matrix and the emergence of the compact extradimensions from the fluctuations. Throughout this paper, our results are enlighten by numerical simulations. In particular, we drawn the geometry of the compact extradimension manifold emerging in our approach.\
*Throughout this paper, we consider the unit system such that $\hbar=c=G=1$ ($\ell_P=t_P=m_P=1$ for 