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 m2 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 gr process. We calculate the spectrum of such a modulated gr 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 gr process and on a factor which describes the temperature dependence of 1/f noise.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 DOI:
 10.48550/arXiv.1201.4162
 arXiv:
 arXiv:1201.4162
 Bibcode:
 2012arXiv1201.4162G
 Keywords:

 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 12 pages, 4 figures This paper has been withdrawn by the author due to an erroneous application of the equipartition theorem in the absorption and emission processes