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

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.

Revtex 4-1, 14 pages, 2 figures. Final published version

References in corpus (4)

• The transfer of energy between electrons and ions in solids
• Geometrization of Quantum Mechanics
• Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence
• Ab Initio Molecular Dynamics on the Electronic Boltzmann Equilibrium Distribution

Cited by in corpus (5)

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• Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence
• Hybrid quantum-classical dynamics of pure-dephasing systems
• Effective nonlinear Ehrenfest hybrid quantum-classical dynamics
• Non-adiabatic effects within a single thermally-averaged potential energy surface: Thermal expansion and reaction rates of small molecules