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Trapped Ion Quantum Computing

Van der Waals interaction at short and long distances: a pedagogical path from stationary to time-dependent perturbation theory

arXiv
Authors: L. Saba, C. D. Fosco

Year

2025

Paper ID

36120

Status

Preprint

Abstract Read

~2 min

Abstract Words

95

Citations

N/A

Abstract

The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. In this pedagogical article, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework that connects both limiting cases while offering a clear conceptual picture suitable for advanced quantum mechanics courses.

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  • The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.23517 [2] arXiv https://arxiv.org/abs/2512.23517 [3] Publisher https://arxiv.org/abs/2512.23517

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