  Background: Microscopic mean-field approaches have been successful in
describing the most probable reaction outcomes in low-energy heavy-ion
reactions. However, those approaches are known to severely underestimate
dispersions of observables around the average values that has limited their
applicability. Recently it has been shown that a quantal transport approach
based on the stochastic mean-field (SMF) theory significantly improves the
description, while its application has been limited so far to fragment mass and
charge dispersions.
  Purpose: In this work, we extend the quantal transport approach based on the
SMF theory for relative kinetic energy dissipation and angular momentum
transfer in low-energy heavy-ion reactions.
  Results: As the first application of the proposed formalism, we consider the
radial linear momentum dispersion, neglecting the coupling between radial and
angular momenta. We analyze the total kinetic energy (TKE) distribution of
binary reaction products in the $^{136}$Xe+$^{208}$Pb reaction at
$E_\mathrm{c.m.}=526$ MeV and compare with experimental data. From time
evolution of single-particle orbitals in TDHF, the radial diffusion coefficient
is computed on a microscopic basis, while a phenomenological treatment is
introduced for the radial friction coefficient. By solving the quantal
diffusion equation for the radial linear momentum, the dispersion of the radial
linear momentum is obtained, from which one can construct the TKE distribution.
We find that the calculations provide a good description of the TKE
distribution for large values of energy losses, TKEL $\gtrsim$ 150 MeV.
However, the calculations underestimate the TKE distribution for smaller energy
losses. Further studies are needed to improve the technical details of
calculations.
  (Shortened due to the word limit)
