Quantum theory of flicker noise: the 1/f law as a lower bound on the voltage power spectrum

An approach to the problem of 1/f voltage noise observed in all conducting media is developed based on an uncertainty relation for the Fourier-transformed signal. It is shown that the quantum indeterminacy caused by non-commutativity of observables at different times sets a lower bound on the power spectrum of voltage fluctuations. Using the Schwinger-Keldysh method, this bound is calculated explicitly in the case of unpolarized free-like charge carriers, and is found to have a 1/f low-frequency asymptotic. It is demonstrated also that account of the charge carrier interaction with phonons results in a shift of the frequency exponent from unity. A comparison with the experimental data on 1/f noise in InGaAs quantum wells and high-temperature superconductors is made which shows that the observed noise levels are only a few times as high as the bound established.