Localization of a quantum particle in a classical one-component plasma. II. Dynamic Disorder and Temporal Decorrelation

We extend the static theory of disorder-induced exponential decay of the averaged Green function of a quantum charged particle in a classical one-component plasma to the dynamic regime by incorporating the temporal evolution of the ionic density fluctuations within the random phase approximation. The dynamic potential correlator is derived from the fluctuation-dissipation theorem and the Kramers--Kronig relations. Within the eikonal (straight-line) approximation, the effective disorder strength is expressed through the dielectric function of the ion plasma. For particles moving faster than the ion thermal speed, the static Coulomb logarithm is recovered, with the large-distance cutoff replaced by the dynamic scale $v/\omega_{pi}$. For slow particles, the Coulomb logarithm disappears completely and the disorder strength becomes proportional to the velocity, leading to a fundamentally different scaling of the localization length. In particular, the strong-disorder length diverges as $k^{-1/3}$ for $v\ll v_{\mathrm{th}}$, whereas it saturates in the static limit, indicating that ultra-slow particles are not exponentially localized in a dynamic plasma. A crossover between the quasi-static and dynamic regimes occurs when the particle speed becomes comparable to the ion thermal speed.