Electronic energy loss in tungsten collision cascades: A quantum statistical study of force scales, friction, and stopping

Electronic stopping in collision cascades is formulated as a problem of driven quantum statistical work. The Keldysh influence functional, obtained by eliminating electronic degrees of freedom along the closed time contour, provides a common parent for both equilibrium electronic friction and nonequilibrium stopping. Two controlled reductions of this functional are evaluated from first principles for tungsten: an equilibrium phonon linewidth projection and an adiabatically subtracted real time stopping calculation. These reductions share mechanical units but differ substantially, because they represent different projections of the retarded electronic force response. The linear low velocity stopping law is shown to be a retarded sector observable that does not imply an equilibrium Langevin noise; a driven stopping tangent can, therefore, exist without the fluctuation–dissipation relation needed to construct a complete electronic thermostat. A force scale comparison on cascade relevant geometries shows that empirical potential errors can exceed the electronic loss force, so that resolving the nonadiabatic correction requires an accurate conservative surface. Projection onto a cascade trajectory reveals that the stopping active population is small and concentrated in the early ballistic stage. We show that the electronic response of a tungsten cascade is sparse, structured, and regime dependent, rather than representable by a single scalar damping coefficient, and that whereas the equilibrium phonon linewidth reduction supports an equilibrium Langevin closure for thermal lattice motion, the driven stopping reduction provides a deterministic loss law for ballistic recoils. Neither can substitute for the other.