We calculate the frequency-dependent mobility of the Holstein polaron in one dimension near the adiabatic limit using the method based on dynamical quantum typicality, as well as the quantum-classical method. The agreement between fully quantum and quantum-classical solutions is very good. The most prominent feature is the appearance of a zero-frequency peak in the mobility, in addition to the displaced peak associated to the precursors of Anderson localization. The zero-frequency peak cannot be obtained within the phenomenological transient localization approach, which is often used in a semiquantitative description of charge transport in quasi-one-dimensional organic semiconductors.

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• Charge dynamics
• Electrical conductivity
• Electron-phonon coupling
• Semiconductors
• Many-body techniques
• Methods in transport