3 research outputs found
Quantum Theory of Reactive Scattering in Phase Space
We review recent results on quantum reactive scattering from a phase space
perspective. The approach uses classical and quantum versions of normal form
theory and the perspective of dynamical systems theory. Over the past ten years
the classical normal form theory has provided a method for realizing the phase
space structures that are responsible for determining reactions in high
dimensional Hamiltonian systems. This has led to the understanding that a new
(to reaction dynamics) type of phase space structure, a {\em normally
hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase
space structures governing reaction dynamics are built. The quantum normal form
theory provides a method for quantizing these phase space structures through
the use of the Weyl quantization procedure. We show that this approach provides
a solution of the time-independent Schr\"odinger equation leading to a (local)
S-matrix in a neighborhood of the saddle point governing the reaction. It
follows easily that the quantization of the directional flux through the
dividing surface with the properties noted above is a flux operator that can be
expressed in a "closed form". Moreover, from the local S-matrix we easily
obtain an expression for the cumulative reactio probability (CRP).
Significantly, the expression for the CRP can be evaluated without the need to
compute classical trajectories. The quantization of the NHIM is shown to lead
to the activated complex, and the lifetimes of quantum states initialized on
the NHIM correspond to the Gamov-Siegert resonances. We apply these results to
the collinear nitrogen exchange reaction and a three degree-of-freedom system
corresponding to an Eckart barrier coupled to two Morse oscillators.Comment: 59 pages, 13 figure