@Hanada] that under these conditions the matrix brane dynamics involves chaotic motions. The fermionic string is then driven by a chaotic system. In previous papers [@Viennot2; @Aubourg; @Aubourg2] we have shown that quantum systems driven by chaotic flows are distinguished from quantum systems driven by random noises by a phenomenon called horizon of coherence, i.e. a duration at the beginning of the dynamics in which the quantum coherence is sustained before to fall with an increase of the entropy. In the present paper, we want to study this phenomenon for a fermionic string in contact with a D2-brane. Moreover we have proposed in [@Viennot3] a natural mathematical approach to study quantum systems driven by chaotic flows, based on the Schrödinger-Koopman formalism [@Sapin; @Jauslin; @Gay]. This formalism is a generalization of the Floquet theory for which we have shown [@Viennot4] that it has similarities with the classical string theory. In particular, a closed extradimension must be added to the control manifold (playing the role of the space) in the context of this Floquet theory. In this paper, we want to show that by a similar mechanism, compact extradimensions emerge from the quantum chaotic fluctuations from the viewpoint of the fermionic string 