Dynamics of mean spherical model with correlated noise

The dynamics of the mean spherical model [1, 2, 3] with a dissipative term and a correlated noise is investigated. This noise obeys a fractional brownian motion [4] with Hurst index $H$, and some mathematical techniques are proposed to obtain asymptotically exact results for large times. The analysis is based on the two-time autocorrelation and response function, and the results are compared to the work of Godr?che-Luck [5], where the noise is uncorrelated (it is worth noting that this problem has been considered before [6]). Comparing the two dynamics (which differ in the nature of the noise only), the present case shows a richer behavior, which is expected due to the presence of an extra parameter $H$; nevertheless, one can also observe the realization of some non-trivial interplay between dissipative part and noise term.

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