A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?

TL;DR

This paper examines the fundamental trade-off in semiclassical electrodynamics between achieving accurate short-range Coulomb interactions and maintaining causality in energy transfer simulations, revealing an inherent paradox.

Contribution

It highlights the conflicting requirements in semiclassical approaches for energy transfer, showing that improving one aspect compromises the other.

Findings

Quantum-classical mismatch causes causality violations.

Classical Coulomb treatment preserves causality but reduces accuracy.

Trade-off between interaction accuracy and causality enforcement.

Abstract

We investigate two key representative semiclassical approaches for propagating resonant energy transfer between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell-Liouville equations. On the one hand, when the electromagnetic (EM) field is treated classically and Coulomb interactions are treated quantum-mechanically, we find that a quantum-classical mismatch leads to a violation of causality, i.e., the acceptor can be excited before the retarded EM field arrives. On the other hand, if we invoke a classical intermolecular Coulomb operator, we find that the energy transfer in the near field loses quantitative accuracy compared with F\"orster theory, even though causality is strictly obeyed. Thus, our work raises a fundamental paradox when choosing a semiclassical electrodynamics algorithm. Namely, which is more important: Accurate short range interactions or long range causality? Apparently, one cannot have one's cake and eat it too.