The Quantum Mechanical Oscillator as a Possible Source of 1/f Fluctuations

Abstract

We investigate consecutive absorption or emission of photons of the quantum mechanical harmonic oscillator as a possible source of 1/f fluctuations. Separating the absorption and emission process, we show that consecutively absorbed or emitted photons give rise to an intermittent stochastic process; thereby fluctuating clusters of photons are intermitted by distinct breaks. Let the number of photons in a cluster be m and the cluster size distribution be pm. We find that the intermittent process with a cluster size distribution pm proportional to m-2 generates a pure 1/f spectrum. We show that 1/f fluctuations are present in thermal equilibrium but average out to zero. As an example we investigate phonons as a possible origin of 1/f fluctuations in an extrinsic semiconductor. Acoustic phonons always produce a change in the volume; this affects the donor ionization energy modulating also the g-r process. We calculate the spectrum of such a modulated g-r process; thereby the intermittent character of phonon activity is identified as the origin of 1/f fluctuations. The Hooge parameter is found to depend on the mean number of phonons comprised in a cluster, on the modulation depth of the g-r process and on a factor which describes the temperature dependence of 1/f noise.