Localization of a quantum particle in a classical one-component plasma.III. Mutual coherence and coherence degradation in Coulomb-disordered media

TL;DR

This paper derives the mutual coherence function for electron beams in Coulomb-disordered media, revealing how disorder affects coherence length and its energy dependence, with implications for electron microscopy and related fields.

Contribution

It introduces a universal relation for coherence length in Coulomb-disordered media and connects transverse coherence decay with localization phenomena, extending to relativistic regimes.

Findings

Coherence length scales as λ_D √(ℓ/L), linking disorder and coherence.

Energy dependence of coherence differs between static and dynamic regimes.

Disorder-induced phase decorrelation impacts high-resolution electron microscopy.

Abstract

We derive the mutual coherence function of an electron beam propagating through a static or dynamic Coulomb-disordered medium and show that its decay introduces an intrinsic coherence-reduction mechanism relevant for electron microscopy in Coulomb-disordered media. Using the Efimov path-integral formalism, the coherence length $\rho_c$ is expressed through the same disorder correlator that governs the single-particle localization length $\ell$. For both a static electrolyte and a dynamic plasma we obtain a universal relation $\rho_c \sim \lambda_D \sqrt{\ell/L}$, where $\lambda_D$ is the Debye length and $L$ the sample thickness. In the static case $\ell\propto k^{2}$ (electron momentum), whereas in the dynamic slow-particle regime $\ell\propto k$, leading to qualitatively different energy dependences of the coherence scale. The ion thermal velocity cancels out in the final expression, demonstrating a formal connection between transverse coherence decay and longitudinal localization phenomena. Exact analytical results are given for the phase structure function of a model electrolyte, and numerical estimates indicate that disorder-induced phase decorrelation may contribute appreciably to the attenuation of high-spatial-frequency contrast under experimentally relevant liquid-cell electron microscopy conditions. Possible implications for cryo-EM, disordered liquids, soft condensed matter, and biological media are discussed. In an appendix we extend the theory to the relativistic regime relevant for transmission electron microscopy.