Passive-reflector bounds and robust bilateral nonequilibrium Casimir repulsion
Abstract
Nonequilibrium electromagnetic fluctuations can generate repulsive Casimir--Lifshitz pressures, but optimizing a cavity at one operating point does not establish that the repulsion survives uncertainty or exceeds ordinary far-field radiation pressure. We formulate a two-sided biased-semiconductor cavity as a constrained max--min problem that maximizes the smaller outward pressure on its two reflectors. In the optically thick-slab limit, identical reflectors admit a symmetric global optimizer, and a passive-reflector bound separates cavity enhancement from the driven far-field plateau. At 300 K, a biased-GaAs cavity with ±10 nm gap uncertainty and ±0.005 drive uncertainty sustains a worst-case pressure of 2.257 mPa with ideal reflectors. Reoptimization with a causal gold response retains 2.164 mPa. The nominal and robust optima lie within 2 nm of one another, so the main value of the max--min calculation here is a quantitative performance certificate rather than a large geometric redesign. A full finite-slab calculation and an alternative published GaAs response change the reported pressures by at most 1.60×10−3% and 4.44×10−2%, respectively. These results establish a reproducible design bound for bilateral nonequilibrium repulsion under dimensional, drive, reflector, and optical-model variations.
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BibTeX
@misc{khodja2026passivereflector,
title = {{Passive-reflector bounds and robust bilateral nonequilibrium Casimir repulsion}},
author = {Mohamed R. Khodja and Belkacem E. Khodja},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02471},
eprint = {2610.02471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02471},
}
RIS
TY - UNPB
TI - Passive-reflector bounds and robust bilateral nonequilibrium Casimir repulsion
AU - Mohamed R. Khodja
AU - Belkacem E. Khodja
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.02471
UR - https://arxiv.org/abs/2610.02471
AB - Nonequilibrium electromagnetic fluctuations can generate repulsive Casimir--Lifshitz pressures, but optimizing a cavity at one operating point does not establish that the repulsion survives uncertainty or exceeds ordinary far-field radiation pressure. We formulate a two-sided biased-semiconductor cavity as a constrained max--min problem that maximizes the smaller outward pressure on its two reflectors. In the optically thick-slab limit, identical reflectors admit a symmetric global optimizer, and a passive-reflector bound separates cavity enhancement from the driven far-field plateau. At 300 K, a biased-GaAs cavity with ±10 nm gap uncertainty and ±0.005 drive uncertainty sustains a worst-case pressure of 2.257 mPa with ideal reflectors. Reoptimization with a causal gold response retains 2.164 mPa. The nominal and robust optima lie within 2 nm of one another, so the main value of the max--min calculation here is a quantitative performance certificate rather than a large geometric redesign. A full finite-slab calculation and an alternative published GaAs response change the reported pressures by at most 1.60×10^−3% and 4.44×10^−2%, respectively. These results establish a reproducible design bound for bilateral nonequilibrium repulsion under dimensional, drive, reflector, and optical-model variations.
ER -