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

Kinetic energy dissipation and fluctuations in strongly-damped heavy-ion collisions within the stochastic mean-field approach