Fokker-Planck operator

Appendix 3. Eigenvalues of the Inhomogeneous Fokker-Planck Operator... 

Drozdov and Tucker have recently criticized the VTST method claiming that it does not bound the exact rate constant. Their argument was that the reactive flux method in the low barrier limit, is not identical to the lowest nonzero eigenvalue of the corresponding Fokker-Planck operator, hence an upper bound to the reactive flux is not an upper bound to the true rate. As aheady discussed above, when the barrier is low, the definition of the rate becomes problematic. All that can be said is that VTST bounds the reactive flux. Whenever the reactive flux method fails, VTST will not succeed either. 

For a specified form of the Fokker-Planck operator L(x), one can find an explicit solution W(x, t) of the FFPE (19) through separation of variables. Indeed, inserting the separation ansatz... 

In the notation of Section V.A, the Fokker-Planck operator driving the the probability function p(x, v, t) can be split into the sum of an unperturbed part... 

In order to apply the AEP of Chapter II, we separate the Fokker-Planck operator T on (5.8) into an unperturbed part Fq and a perturbation part Fj, so that... 

Garcia-Palacios JL, Svedlindh P (2001) Derivation of the basic system equations governing superparamagnetic relaxation by the use of the adjoint Fokker-Planck operator. Phys Rev B 63 172417-1-172417/4... 

So far we have considered the planar rotator model. However, the above equations can readily be generalized to rotation in space. Here, the space coordinate is the polar angle i) and the Fokker-Planck operator for normal rotational diffusion assumes the form [8] [cf. Eq. (80)]... 

We suppose that a small probing held Fj, having been applied to the assembly of dipoles in the distant past (f = —oo) so that equilibrium conditions have been attained at time t = 0, is switched off at t = 0. Our starting point is the fractional Smoluchowski equation (172) for the evolution of the probability density function W(i), cp, t) for normal diffusion of dipole moment orientations on the unit sphere in configuration space (d and (p are the polar and azimuthal angles of the dipole, respectively), where the Fokker-Planck operator LFP for normal rotational diffusion in Eq. (8) is given by l j p — l j /> T L where... 

Fokker-Planck Operators The Graham-Haken Conditions... 

Fokker-Planck Operators The Graham-Haken Conditions The general operator of a FP operator is... 

---