number of D0-branes is $N=11$ (for the fuzzy hyperboloid the cutoff is $N=11$). The vertical line indicates the horizon of coherence. The initial condition for the string is $|\psi(t=0) {\rangle \hspace{-0.2em} \rangle}= \frac{1}{\sqrt 2}(|\uparrow \rangle+|\downarrow \rangle) \otimes (1,0,...,0)$.](entropySphere.eps "fig:"){width="6.4cm"}\
![\[cohe\] Coherence and von Neumann entropy of the spin mixed state of the fermionic string, for $X_0$ without fluctuation ($\rho_0$) and for $X$ with fluctuations ($\overline \rho$), with fuzzy sphere, torus and hyperboloid. The initial fluctuations are choosen following a gaussian law with $\sigma=0.01$. The number of D0-branes is $N=11$ (for the fuzzy hyperboloid the cutoff is $N=11$). The vertical line indicates the horizon of coherence. The initial condition for the string is $|\psi(t=0) {\rangle \hspace{-0.2em} \rangle}= \frac{1}{\sqrt 2}(|\uparrow \rangle+|\downarrow \rangle) \otimes (1,0,...,0)$.](coheTorus.eps "fig:"){width="6.4cm"} ![\[cohe\] Coherence and von Neumann entropy of the spin mixed state of the fermionic string, for $X_0$ without fluctuation ($\rho_0$) and for $X$ with fluctuations ($\overline \rho$), with fuzzy sphere, torus and hyperboloid. The initial fluctuations are choosen following a gaussian law with $\sigma=0.01$. The number of D0-branes is $N=11$ (for the fuzzy hyperboloid the cutoff is $N=11$). The vertical line indicates the horizon of coherence. The initial condition for the string is $|\psi(t=0) {\rangle \hspace{-0.2em} \rangle}= 