# Understanding the Nature of Mean-Field Semiclassical Light-Matter Dynamics: An Investigation of Energy Transfer, Electron-Electron Correlations, External Driving and Long-Time Detailed Balance

## TL;DR

This paper compares different semiclassical light-matter interaction models to determine their reliability in simulating energy transfer and driven dynamics in molecular systems, revealing that simpler mean-field approaches can outperform full quantum treatments in some cases.

## Contribution

It systematically evaluates multiple semiclassical schemes for light-matter interactions, highlighting their strengths and limitations in modeling energy transfer and external driving effects.

## Key findings

- Hamiltonian #I performs best for resonance energy transfer.
- Hamiltonian #II is stable but fails at short distances.
- Full quantum treatment can overestimate energy under external driving.

## Abstract

Semiclassical electrodynamics is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting different molecules plus a classical transverse E-field; we will call this Hamiltonian #I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body E-field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian #II. Moreover, one can also mix these two Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a pair of identical two-level systems (TLSs) undergoing either resonance energy transfer (RET) or collectively driven dynamics. While all approaches perform reasonably well when there is no strong external excitation, we find that no single approach is perfect for all conditions. Each method has its own distinct problems: Hamiltonian #I performs best for RET but behaves in a complicated manner for driven dynamics. Hamiltonian #II is always stable, but obviously fails for RET at short distances. One key finding is that, under externally driving, a full configuration interaction description of Hamiltonian #I strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field treatment.