A Stochastic Model of 1⁄f Phonon-Number Fluctuations

Abstract

We propose a stochastic model of phonon-number fluctuations that allows to simulate 1⁄f-like behavior. The fluctuation process is described as a random walk on the ladder of energy levels of a harmonic oscillator. Two characteristic time scales are involved in the process: the mean life time of states τ_l and the correlation time τ_c. When the ratio τ_c⁄τ_l is large, the 1⁄f-like spectrum is observed within the frequency range 1⁄τ_c<f<1⁄τ_l. Conditions for large values of the ratio are discussed.