Electronic decoherence along a single nuclear trajectory

We describe an approach to subsystem decoherence without the usual tracing out of the environment. The subsystem of focus is described entirely by a pure state evolving nonunitarily along a single classical trajectory of its environment. The approach is deduced from the exact factorization framework for arbitrary systems of electrons and nuclei. The nonunitarity of the electronic dynamics arises exclusively from nonadiabatic correlations between electrons and nuclei. We demonstrate that the approach correctly describes the coherence gain and the subsequent decoherence for the example of a nuclear trajectory passing through an avoided crossing, the prototypical case where single-trajectory Ehrenfest dynamics fails to produce decoherence.