Hamiltonian systems transport

For time-dependent Hamiltonian systems we chose in Section IVB to use a normal form that decouples the reactive mode from the bath modes, but does not attempt a decoupling of the bath modes. This procedure is always safe, but in many cases it will be overly cautious. If it is relaxed, the dynamics within the center manifold is also transformed into a (suitably defined) normal form. This opens the possibility to study the dynamics within the TS itself, as has been done in the autonomous case, for example in Ref. 107. One can then try to identify structures in the TS that promote or inhibit the transport from the reactant to the product side. 

Meiss, J.D. and Ott, E. (1985). Markov-tree model of intrinsic transport in Hamiltonian systems, Phys. Rev. Lett. 55, 2741-2744. 

II. Anomalous Transport in Hamiltonian Systems with Mixed Phase Space... 

II. ANOMALOUS TRANSPORT IN HAMILTONIAN SYSTEMS WITH MIXED PHASE SPACE... 

MD simulations with a constant energy is nothing but Hamiltonian dynamics. Recent accumulation of MD simulations will certainly contribute to our further understanding of Hamiltonian systems, especially in higher dimensions. The purpose of this section is to sketch briefly how the slow relaxation process emerges in the Hamiltonian dynamics, and especially to show that transport properties of phase-space trajectories reflect various underlying invariant structures. 

S. Wiggins, Physica, D44, 471 (1990). On the Geometry of Transport in Phase Space 1. Transport in /fe-Degree-of-Freedom Hamiltonian Systems, 2 s k < . 

All discussions of transport processes currently available in the literature are based on perturbation theory methods applied to kinetic pictures of micro-scattering processes within the macrosystem of interest. These methods do involve time-dependent hamiltonians in the sense that the interaction operates only during collisions, while the wave functions are known only before and after the collision. However these interactions are purely internal, and their time-dependence is essentially implicit the over-all hamiltonian of the entire system, such as the interaction term in Eq. (8-159) is not time-dependent, and such micro-scattering processes cannot lead to irreversible changes of thermodynamic (ensemble average) properties. 

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