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 nonadiabatic 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 analyzing the appearance of the pointer basis to which the system decoheres, which for our example is composed of the eigenstates of the electronic Hamiltonian.
Highlights
The Schrödinger equation for a combined system of electrons and nuclei is generally too complex and involves too many degrees of freedom to be solvable, neither analytically nor by numerical methods
Most approaches can be described in two steps: first, a partial deconstruction of the quantum mechanics (QM) of the total system which simplifies the model, and a reconstruction that aims to recover the essential properties of the total Schrödinger equation lost in the deconstruction process
The first one, called Born-Oppenheimer molecular dynamics (BOMD), is far away from the total Schrödinger equation for electrons and nuclei, as electrons are assumed to remain in the ground state for all times
Summary
The Schrödinger equation for a combined system of electrons and nuclei is generally too complex and involves too many degrees of freedom to be solvable, neither analytically nor by numerical methods. Many different proposals tackle the difficulty of re-incorporating into HQCD models the essential properties of the total Schrödinger equation that have been lost One of these properties is the decoherence phenomenon in the electronic subsystem. In the context of HQCD, decoherence is understood as the fact that the neglected wave functions in the classical limit (i.e. those of the nuclei) rapidly lose overlap in time, leading to the destruction of superpositions in the quantum subsystem, i.e. forcing the electronic wave functions into a mixture of pure states [3, 5].
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