Phase portrait of the noiseless damped dynamics corresponding to the linear Langevin equation (3) in (a) the unstable reactive degree of freedom, (b) a transverse stable degree of freedom, and (c) an overdamped transverse degree of freedom.
A random instance of the TS trajectory in a system with degrees of freedom, projected onto (a) configuration space, (b) velocity space, (c) the reactive degree of freedom, and (d) the transverse degree of freedom. Units have been chosen so that , . The transverse frequency is , and friction is isotropic, with .
The instance of the TS trajectory shown in Fig. 2 and a transition path under the influence of the same noise. Trajectories are projected onto (a) the reactive degree of freedom, (b) the transverse degree of freedom, and (c) configuration space. At the lower end of each column is a projection into the corresponding phase-space plane, disregarding time. The instantaneous positions of the moving coordinate axes (dotted) and, in (a), of the invariant manifolds (dashed) are shown at , at , and at the unique reaction time where the TS is crossed. The solid line at indicates the moving TS. The curves in the top faces of each panel illustrates the dynamics of the transition path in relative coordinates , [not to scale in (a), for graphical reasons].
Variances (34) of stable (solid curve) and unstable (dashed curve) components the TS trajectory in one dimension.
Variance (36) of the position coordinate of the TS trajectory in one dimension.
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