Chaos, decoherence and emergent extradimensions in D-brane dynamics with fluctuations

Understand

We study, by using tools of the dynamical system theory, a fermionic string streched from a non-commutative D2-brane (stack of D0-branes in the BFSS model) to a probe D0-brane as a quantum system driven by a chaotic system, the (classical and quantum) chaos being induced in the D2-brane dynamics by quantum fluctuations.

• We show that this dynamics with fluctuations induces a decoherence phenomenon on the reduced density matrix of the fermionic string which is characteristic of the chaotic behaviour since it presents an horizon of coherence.
• Moreover we show that this dynamics is associated with an invariant torus which involves extradimensions emerging from the fluctuations for the viewpoint of the fermionic string, extending a three dimensional space by six compact dimensions.
• The situation studied can be considered as a model of qubit (supported by the fermionic string) in interaction with a quantum black hole (modelized by the non-commutative D2-brane).