Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum

TL;DR

This paper develops a quantum transition state theory using quantum normal forms, enabling efficient computation of quantum reaction rates and resonances, and links classical and quantum phase space structures.

Contribution

It introduces a general algorithm for quantum normal form expansion, bridging classical and quantum transition state theories in phase space.

Findings

Efficient computation of quantum reaction rates and resonances.

Quantum normal form reduces to classical form in the classical limit.

Phase space structures underpin quantum scattering and resonance wavefunctions.

Abstract

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's transition state theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.