Ehrenfest statistical dynamics in chemistry: study of decoherence effects

TL;DR

This paper investigates decoherence effects within Ehrenfest Statistical Dynamics (ESD) for a simple molecular model, demonstrating that ESD captures decoherence and pointer basis formation, challenging the view that Ehrenfest models lack this feature.

Contribution

It extends previous work by analyzing decoherence and pointer basis emergence in ESD, providing a rigorous statistical perspective on Ehrenfest dynamics in a realistic molecular system.

Findings

Decoherence occurs in ESD as shown by purity reduction.

Pointer basis aligns with electronic Hamiltonian eigenstates.

Ehrenfest dynamics can describe decoherence phenomena.

Abstract

In previous works, we introduced a geometric route to define our Ehrenfest Statistical Dynamics (ESD) and we proved that, for a simple toy-model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to non-adiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analysing the appearance of the pointer basis to which the system decoheres, which for our example is composed by the eigenstates of the electronic Hamiltonian.