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We investigate transport properties of quantized chaotic systems in the shortwavelength limit. We focus on non-coherent quantities such as the Drudeconductance, its sample-to-sample fluctuations, shot-noise and the transmissionspectrum, as well as coherent effects such as weak localization. We show howthese properties are influenced by the emergence of the Ehrenfest time scale$\tE$. Expressed in an optimal phase-space basis, the scattering matrixacquires a block-diagonal form as $\tE$ increases, reflecting the splitting ofthe system into two cavities in parallel, a classical deterministic cavity(with all transmission eigenvalues either 0 or 1) and a quantum mechanicalstochastic cavity. This results in the suppression of the Fano factor forshot-noise and the deviation of sample-to-sample conductance fluctuations fromtheir universal value. We further present a semiclassical theory for weaklocalization which captures non-ergodic phase-space structures and preservesthe unitarity of the theory. Contrarily to our previous claim [Phys. Rev. Lett.94, 116801 (2005)], we find that the leading off-diagonal contribution to theconductance leads to the exponential suppression of the coherent backscatteringpeak and of weak localization at finite $\tE$. This latter finding issubstantiated by numerical magnetoconductance calculations.Comment: Typos in central eqns corrected (this paper supersedes  cond-mat/0509186) 20page

Semiclassical theory of quantum chaotic transport: Phase-space splitting, coherent backscattering, and weak localization