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

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

2007-08-03

arxiv.org/abs/0708.0511v2

Nonlinearity, 21 (2008) R1-R118

Nonlinear Sciences

Chaotic Dynamics

132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008) R1-R118

Scientific paper

10.1088/0951-7715/21/1/R01

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.

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