| A great number of mesoscopic systems can be modeled by noisy maps. An important property of such models is the possiblity of noise-induced escape from an otherwise invariant set. This can be expressed by the mean first exit time, which is therefore critical in characterising the stability of the corresponding set under noise. Here, we consider the time evolution of the probability density of noisy maps which is governed by the iteration of the Perron-Frobenius (PF) operator. In the weak noise limit, the corresponding evolution operator can be semiclassicaly expanded, truncated to the first order and solved by steepest-descent integration. This leads us to the expression of a general symplectic deterministic map whose trajectories yield the contributions to the first order semiclassical evolution operator. We show that this general deterministic map is useful to compute temporal properties of noisy maps. |
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