Universal and rigorous asymptotic convergence of standard macroscopic quantum electrodynamics to the modified Langevin noise formalism
Abstract
The standard Langevin noise formalism (LNF) is a well-established approach for macroscopic quantum electrodynamics in unbounded lossy media, and accordingly, its application to finite objects requires endowing the surrounding vacuum with a fictitious absorption that is taken to asymptotically vanish. Existing justifications for such a singular limiting procedure have been mainly restricted to phenomena governed by vacuum fluctuations and medium-induced interactions (Casimir-Polder forces, thermal radiation, quantum emitter dynamics, etc.), thereby strictly excluding scenarios that involve the scattering of external quantum radiation. Conversely, the modified Langevin noise formalism (MLNF) has recently been established as the complete canonical quantum theory for arbitrary macroscopic systems and electromagnetic processes, entirely bypassing the need for limiting procedures, treating incident quantum radiation fields as independent degrees of freedom, and exactly reducing to the LNF for unbounded media. In this work, we demonstrate that the LNF limiting procedure is universally valid by showing that it recovers any physical prediction of the MLNF across all regimes, including arbitrary quantum scattering processes. Specifically, we introduce a suitable mapping associating any MLNF state and observable with a corresponding entity within the LNF augmented by fictitious vacuum absorption. We then rigorously prove that, as the fictitious absorption tends to zero, every LNF matrix element constructed via this mapping exactly converges to its MLNF original, so that the limiting procedure establishes the asymptotic convergence of the LNF to the MLNF.
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BibTeX
@misc{ciattoni2026universal,
title = {{Universal and rigorous asymptotic convergence of standard macroscopic quantum electrodynamics to the modified Langevin noise formalism}},
author = {A. Ciattoni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05202},
eprint = {2610.05202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05202},
}
RIS
TY - UNPB
TI - Universal and rigorous asymptotic convergence of standard macroscopic quantum electrodynamics to the modified Langevin noise formalism
AU - A. Ciattoni
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05202
UR - https://arxiv.org/abs/2610.05202
AB - The standard Langevin noise formalism (LNF) is a well-established approach for macroscopic quantum electrodynamics in unbounded lossy media, and accordingly, its application to finite objects requires endowing the surrounding vacuum with a fictitious absorption that is taken to asymptotically vanish. Existing justifications for such a singular limiting procedure have been mainly restricted to phenomena governed by vacuum fluctuations and medium-induced interactions (Casimir-Polder forces, thermal radiation, quantum emitter dynamics, etc.), thereby strictly excluding scenarios that involve the scattering of external quantum radiation. Conversely, the modified Langevin noise formalism (MLNF) has recently been established as the complete canonical quantum theory for arbitrary macroscopic systems and electromagnetic processes, entirely bypassing the need for limiting procedures, treating incident quantum radiation fields as independent degrees of freedom, and exactly reducing to the LNF for unbounded media. In this work, we demonstrate that the LNF limiting procedure is universally valid by showing that it recovers any physical prediction of the MLNF across all regimes, including arbitrary quantum scattering processes. Specifically, we introduce a suitable mapping associating any MLNF state and observable with a corresponding entity within the LNF augmented by fictitious vacuum absorption. We then rigorously prove that, as the fictitious absorption tends to zero, every LNF matrix element constructed via this mapping exactly converges to its MLNF original, so that the limiting procedure establishes the asymptotic convergence of the LNF to the MLNF.
ER -