Dynamic Eikonal Attenuation and Mutual Coherence of Quantum Particles due to Equilibrium Coulomb Fluctuations
Abstract
We develop a dynamic theory of eikonal attenuation and mutual coherence for a quantum particle propagating through equilibrium Coulomb fluctuations. The one-particle length ℓ is the attenuation length of the ensemble-averaged retarded propagator, not an Anderson localization length or a transport mean free path. For a collisionless classical one-component plasma (OCP), the potential spectrum follows from the fluctuation--dissipation theorem and the RPA dielectric function. In suitable plasma parameter windows, both fast and slow probe regimes are physically meaningful. Fast probes recover the Coulomb logarithm with the dynamical infrared length v/ωp. Slow probes yield G(v)∝ v and, in the controlled weak branch, ℓ∝ k. We derive an exact finite-thickness mutual-coherence expression and a closed slow-regime transverse scaling function. Within the controlled slow-OCP and thick-slab window, the logarithmic two-ray visibility scales as v−1 at fixed transverse separation, in contrast to the v−2 dependence for frozen finite-slab fluctuations. For a symmetric diffusive electrolyte, linearized stochastic density functional theory gives the exact on-shell result Gel(v)=(m2C/ℏ4)arsinh[v/(2Dκ)], where C=kBTq02/(4πεb). For ordinary liquid electrolytes, the slow diffusive limit is inaccessible within the spatial eikonal regime and is therefore a formal asymptote. The physically relevant electrolyte limit is instead that of a fast probe, v≫ Dκ, where the diffusive charge relaxation generates an intrinsic infrared length v/(Dκ2) absent from the quasi-static theory.
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BibTeX
@misc{budkov2026dynamic,
title = {{Dynamic Eikonal Attenuation and Mutual Coherence of Quantum Particles due to Equilibrium Coulomb Fluctuations}},
author = {Yury A. Budkov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.18196},
eprint = {2605.18196},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.18196},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamic Eikonal Attenuation and Mutual Coherence of Quantum Particles due to Equilibrium Coulomb Fluctuations
AU - Yury A. Budkov
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.18196
UR - https://arxiv.org/abs/2605.18196
AB - We develop a dynamic theory of eikonal attenuation and mutual coherence for a quantum particle propagating through equilibrium Coulomb fluctuations. The one-particle length ℓ is the attenuation length of the ensemble-averaged retarded propagator, not an Anderson localization length or a transport mean free path. For a collisionless classical one-component plasma (OCP), the potential spectrum follows from the fluctuation--dissipation theorem and the RPA dielectric function. In suitable plasma parameter windows, both fast and slow probe regimes are physically meaningful. Fast probes recover the Coulomb logarithm with the dynamical infrared length v/ω_p. Slow probes yield G(v)∝ v and, in the controlled weak branch, ℓ∝ k. We derive an exact finite-thickness mutual-coherence expression and a closed slow-regime transverse scaling function. Within the controlled slow-OCP and thick-slab window, the logarithmic two-ray visibility scales as v^−1 at fixed transverse separation, in contrast to the v^−2 dependence for frozen finite-slab fluctuations. For a symmetric diffusive electrolyte, linearized stochastic density functional theory gives the exact on-shell result G_el(v)=(m^2C/ℏ^4)arsinh[v/(2Dκ)], where C=k_BTq_0^2/(4πε_b). For ordinary liquid electrolytes, the slow diffusive limit is inaccessible within the spatial eikonal regime and is therefore a formal asymptote. The physically relevant electrolyte limit is instead that of a fast probe, v≫ Dκ, where the diffusive charge relaxation generates an intrinsic infrared length v/(Dκ^2) absent from the quasi-static theory.
ER -