Electron random walk in ideal phonon gas. Spectra of density matrix evolution and electron mobility 1/f noise

Abstract

The previously derived exact evolution equations for density matrix of electron (quantum particle) in phonon field (boson thermostat) are qualitatively analysed. Their statistical interpretation is explained in detail, and their main symmetry and spectral properties are expounded. In application to the electron's random walk, it is shown that these properties certaimly forbid conventionally assumed Gaussian long-range asymptotic of the walk statistics. Instead, the exact equations imply super-linear dependence of fourth-order cumulant of total electron's path on observation time, which signifies existence of 1/f-type low-frequency fluctuations in electro's diffusivity and mobility. Physical meaning of this result is discussed, along with general origin of 1/f-noise in classical and quantum Hamiltonian many-particle systems.