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We derive analytical expressions for the spectral moments of the dynamicalresponse functions of the Hubbard model using the high-temperature seriesexpansion. We consider generic dimension $d$ as well as the infinite-$d$ limit,arbitrary electron density $n$, and both finite and infinite repulsion $U$. Weuse moment-reconstruction methods to obtain the one-electron spectral function,the self-energy, and the optical conductivity. They are all smooth functions athigh-temperature and, at large-$U$, they are featureless with characteristicwidths of order the lattice hopping parameter $t$. In the infinite-$d$ limit wecompare the series expansion results with accurate numerical renormalizationgroup and interaction expansion quantum Monte-Carlo results. We find excellentagreement down to surprisingly low temperatures, throughout most of thebad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale.The resistivity increases linearly in $T$ at high-temperature withoutsaturation. This results from the $1/T$ behaviour of the compressibility orkinetic energy, which play the role of the effective carrier number. Incontrast, the scattering time (or diffusion constant) saturate at high-$T$. Wefind that $\sigma(n,T) \approx (1-n)\sigma(n=0,T)$ to a very good approximationfor all $n$, with $\sigma(n=0,T)\propto t/T$ at high temperatures. Thesaturation at small $n$ occurs due to a compensation between thedensity-dependence of the effective number of carriers and that of thescattering time. The $T$-dependence of the resistivity displays a knee-likefeature which signals a cross-over to the intermediate-temperature regime wherethe diffusion constant (or scattering time) start increasing with decreasing$T$. At high-temperatures, the thermopower obeys the Heikes formula, while theWiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$.

Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective