Quantum-Acoustical Drude Peak Shift

Quantum acoustics -- a recently developed framework parallel to quantum optics -- establishesa nonperturbative and coherent treatment of the electron-phonon interaction in real space. The quantum-acoustical representation reveals a displaced Drude peak hid ing in plain sight within the venerable Fr\"ohlich model: the optical conductivity exhibits a finite frequency maximum in the far-infrared range and the d.c. conductivity is suppressed. Our results elucidate the origin of the high-temperature absorption peaks in strange or bad metals, revealing that dynamical lattice disorder steers the system towards a non-Drude behavior