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A theory of non-equilibrium (``shot'') noise and high frequency conductancein diffusive mesoscopic conductors with screening is presented. Detailedresults are obtained for two simple geometries, for both large and shortelectron-electron scattering length $l_{ee}$, at frequencies of the order ofthe inverse Thouless time $1/\tau_T$. The conductance and the noise are foundto exhibit significant frequency dependence. For $L \ll l_{ee}$, thehigh-frequency ($\omega\tau_T \gg 1$) shot noise spectral density $S_I(\omega)$approaches a finite value between $2eI/3$ and $2eI$, depending on the screeningproperties of the system, with temperature corrections to $S_I(\omega)$ beinglinear in $T$. However, when $L \gg l_{ee}$, $S_I(\omega)$ grows as$\omega^{1/4}$ (at T=0), is not upper-bound by $2eI$, and has atemperature-dependent component quadratic in $T$. As a result, measurements of$S_I(\omega, T)$ can be utilized as a probe of the strength ofelectron-electron scattering.Comment: 14 pages, 7 figure

Noise properties and ac conductance of mesoscopic diffusive conductors with screening