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The susceptibility of an overdamped Markov system fluctuating in a bistable potential of general form is obtained by analytic solution of the Fokker-Planck equation (FPE) for low noise intensities. The results are discussed in the context of the LRT theory of stochastic resonance. They go over into recent results (Gang Hu et al {em Phys. Lett. A} {bf 172}, 21, 1992) obtained from the FPE for the case of a symmetrical potential, and they coincide with the LRT results (Dykman et al, {em Phys. Rev. Lett.} {bf 65}, 2606, 1990; {em JETP Lett} {bf 52}, 144, 1990; {em Phys. Rev. Lett.} {bf 68}, 2985, 1992) obtained for the general case of bistable systems.
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Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals. In particular it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this article we present a new fitting protocol that uses this correlation to add new additional constraint in Symmetric Infinite Nuclear Matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.
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