Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

TL;DR

This paper investigates how Ehrenfest dynamics causes quantum purity to decrease over time, highlighting its role in modeling decoherence in mixed quantum/classical systems.

Contribution

It introduces a new framework to exactly determine purity changes in statistical Ehrenfest dynamics, revealing its non-preserving nature and implications for decoherence modeling.

Findings

Ehrenfest dynamics reduces quantum purity over time.

Purity evolution depends on quantum state space dimension D.

Number of classical trajectories N influences purity decay.

Abstract

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.