Quantum transport, classically chaotic systems

Rigorous Quantum Rate Theory Versus the Quantized ARRKM Theory A Semiclassical Approximation to the Rigorous Quantum Rate Theory Effective Hamiltonian Approach to Unimolecular Dissociation Wave Packet Dynamics Approach VII. Quantum Transport in Classically Chaotic Systems... 

As shown above, classical unimolecular reaction rate theory is based upon our knowledge of the qualitative nature of the classical dynamics. For example, it is essential to examine the rate of energy transport between different DOFs compared with the rate of crossing the intermolecular separatrix. This is also the case if one attempts to develop a quantum statistical theory of unimolecular reaction rate to replace exact quantum dynamics calculations that are usually too demanding, such as the quantum wave packet dynamics approach, the flux-flux autocorrelation formalism, and others. As such, understanding quantum dynamics in classically chaotic systems in general and quantization effects on chaotic transport in particular is extremely important. 

Here we review some recent results concerning quantum transport in classically chaotic systems, including new results on suppressed quantum transport through cantori, quantum suppression of Arnold diffusion, and faster-than-classical quantum anomalous diffusion. 

This hnding concerning quantum transport in classically chaotic systems sheds new light on quantum effects in unimolecular reaction dynamics. For example, one expects that intramolecular bottlenecks associated with canton, if treated quantum mechanically, would be more effective than in a classical statistical theory even when nh is smaller than the reaction flux crossing the intramolecular dividing surface. Clearly, it would be interesting to examine realistic molecular systems in a similar fashion. 

In this chapter we have reviewed the development of unimolecular reaction rate theory for systems that exhibit deterministic chaos. Our attention is focused on a number of classical statistical theories developed in our group. These theories, applicable to two- or three-dimensional systems, have predicted reaction rate constants that are in good agreement with experimental data. We have also introduced some quantum and semiclassical approaches to unimolecular reaction rate theory and presented some interesting results on the quantum-classical difference in energy transport in classically chaotic systems. There exist numerous other studies that are not considered in this chapter but are of general interest to unimolecular reaction rate theory. 

Recently, Maitra and Heller reexamined quantum transport through cantori [93], including the cases in which nh is actually smaller than the classical flux crossing a particular cantorus. In doing so, they used the Whisker map, which can describe the motion within a chaotic layer near a separatrix in a typical nonintegrable system. The Whisker map is given by... 

To date there are only a few studies of the quantum dynamics associated with classical anomalous diffusion. We consider here a recent study by Brumer and co-workers, who showed that quantum effects can further accelerate classical anomalous diffusion [97]. This is highly counterintuitive, since people tend to believe that in aU cases quantum effects suppress classical chaotic transport. The system they studied is a modified kicked rotor system, whose Hamiltonian is given by... 

---