Chaotic transitions molecular dynamics

In typical molecular dynamics applications with multiple bodies and complicated force laws, the motion is assumed to be chaotic. Ergodic coverage of would then have to arise from the global properties of a chaotic system (sensitivity to initial conditions and transitivity). Liouville s equation,... 

The highly excited and reactive dynamics, the details of which have been made accessible by recently developed experimental techniques, are characterized by transitions between classically regular and chaotic regimes. Now molecular spectroscopy has traditionally relied on perturbation expansions to characterize molecular energy spectra, but such expansions may not be valid if the corresponding classical dynamics turns out to be chaotic. This leads us to a reconsideration of such perturbation techniques and provides the starting point for our discussion. From there, we will proceed to discuss the Gutzwiller trace formula, which provides a semiclassical description of classically chaotic systems. 

There are situations for which the deterministic, macroscopic, reaction-diffusion equations may not provide a correct description of the dynamics. Internal noise or molecular fluctuations can give rise to nucleation events that itjduce transitions between stable states. Fluctuations can be amplified near bifurcation points and in the vicinity of deterministic chaotic dynamics. In such cases the validity of mean-field descriptions must be examined. In addition, if the system size is very small, fluctuations can play an important role since their amplitude is a function of the system size. These considerations prompt one to seek descriptions of non-equilibrium reaction dynamics that incorporate the effects of internal noise and allow one to study the system at a level that is finer than that given by the reaction-diffusion equations. 

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