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We present a mixed quantum–classical framework for the microscopic and non-Markovian modeling of exciton–phonon scattering in solid-state materials and apply it to calculate the optical linewidths of monolayer MoS2. Within this framework, we combine reciprocal-space mixed quantum–classical dynamics with models for the quasiparticle band structure as well as the electron–hole and carrier–phonon interactions, parametrized against ab initio calculations, although noting that a direct interfacing with ab initio calculations is straightforward in principle. We introduce various parameters for truncating the Brillouin zone to select regions of interest. Variations of these parameters allow us to determine linewidths in the limit of asymptotic material sizes. The obtained asymptotic linewidths are found to agree favorably with experimental measurements across a range of temperatures. As such, our framework establishes itself as a promising route toward unraveling the non-Markovian and microscopic principles governing the nonadiabatic dynamics of solids. 

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question of how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity while yielding improved accuracy throughout much (but not all) of parameter space.