x_i(t) \rangle$, for the fuzzy sphere, ellipsoid, torus and the noncommutative plane. Initial conditions for $|\delta x_i(t=0) \rangle$ are choosen following a gaussian law with $\sigma=0.01$. The number of D0-branes is $N=201$ (for the noncommutative plane the cutoff is $N=11$) (simulations show that the thermalization duration grows with $N$).](fluctEllipsoid201.eps "fig:"){width="6.4cm"}\
![\[fluctuations\] Evolution of the amplitudes of the fluctuations $|\delta x_i(t) \rangle$, for the fuzzy sphere, ellipsoid, torus and the noncommutative plane. Initial conditions for $|\delta x_i(t=0) \rangle$ are choosen following a gaussian law with $\sigma=0.01$. The number of D0-branes is $N=201$ (for the noncommutative plane the cutoff is $N=11$) (simulations show that the thermalization duration grows with $N$).](fluctTorus201.eps "fig:"){width="6.4cm"} ![\[fluctuations\] Evolution of the amplitudes of the fluctuations $|\delta x_i(t) \rangle$, for the fuzzy sphere, ellipsoid, torus and the noncommutative plane. Initial conditions for $|\delta x_i(t=0) \rangle$ are choosen following a gaussian law with $\sigma=0.01$. The number of D0-branes is $N=201$ (for the noncommutative plane the cutoff is $N=11$) (simulations show that the thermalization duration grows with $N$).](fluctPlane.eps "fig:"){width="6.4cm"}

We see that the fluctuations evolve until to reach a plateau corresponding to the thermalization of the system (the system with the fluctuations has reached a steady state). The existence of this 