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Failure of Effective Potential Approach: Nucleus-Electron Entanglement in the He-Ion

J. Gemmer·G. Mahler
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Abstract

Entanglement may be considered a resource for quantum-information processing, as the origin of robust and universal equilibrium behaviour, but also as a limit to the validity of an effective potential approach, in which the influence of certain interacting subsystems is treated as a potential. Here we show that a closed three particle (two protons, one electron) model of a He-ion featuring realistic size, interactions and energy scales of electron and nucleus, respectively, exhibits different types of dynamics depending on the initial state: For some cases the traditional approach, in which the nucleus only appears as the center of a Coulomb potential, is valid, in others this approach fails due to entanglement arising on a short time-scale. Eventually the system can even show signatures of thermodynamical behaviour, i.e. the electron may relax to a maximum local entropy state which is, to some extent, independent of the details of the initial state.

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J. Gemmer, G. Mahler. 2002-01-29. Failure of Effective Potential Approach: Nucleus-Electron Entanglement in the He-Ion. https://doi.org/10.1209/epl/i2002-00222-0

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