Abstract
We study the dynamical properties of bistable systems described by the one-dimensional subdiffusive fractional Fokker–Planck equation, for the natural boundary conditions as well as the absorbing boundary conditions. We have investigated the propagators, the auto-correlation function, the survival probability and the lifetime distribution for two model potentials: (1) the quartic double-well potential U 4( x)=(−0.5 x 2+0.25 x 4), and (2) the sextic double-well potential U 6( x)=(−0.75 x 4+0.5 x 6). For both potentials, the evolution of the propagator P( x, t|0,0) shows a trimodal transient, in contrast with the result of the conventional Fokker–Planck Theory.
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