Transition-state dynamics in complex quantum systems
- URL: http://arxiv.org/abs/2105.12073v1
- Date: Tue, 25 May 2021 16:51:30 GMT
- Title: Transition-state dynamics in complex quantum systems
- Authors: G.F. Bertsch and K. Hagino
- Abstract summary: We study the reaction dynamics in complex quantum systems in which the complete mixing of states is hindered by an internal barrier.
The validity of the transition-state theory is questionable when there is no identifiable coordinate associated with the barrier.
We find that the transition-state formula can be derived from the model under some easily justifiable approximations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A model is proposed for studying the reaction dynamics in complex quantum
systems in which the complete mixing of states is hindered by an internal
barrier. Such systems are often treated by the transition-state theory, also
known in chemistry as RRKM theory, but the validity of the theory is
questionable when there is no identifiable coordinate associated with the
barrier. The model consists of two Gaussian Orthogonal Ensembles (GOE) of
internal levels coupled to each other and to the wave functions in the entrance
and decay channels. We find that the transition-state formula can be derived
from the model under some easily justifiable approximations. In particular, the
assumption in transition-state theory that the reaction rates are insensitive
to the decay widths of the internal states on the far side of the barrier is
fulfilled for broad range of Hamiltonian parameters. More doubtful is the
common assumption that the transmission factor $T$ across the barrier is unity
or can be modeled by a one-dimensional Hamiltonian giving $T$ close to unity
above the barrier. This is not the case in the model; we find that the
transmission factor only approaches one under special conditions that are not
likely to be fulfilled without a strong collective component in the
Hamiltonian.
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