On properties of elementary excitations in fractal media

TL;DR

This paper explores how elementary excitations in fractal media follow a variable-order parastatistics, with the order depending on wave number and fractal dimension, affecting fluctuation spectra and potentially explaining 1/f noise.

Contribution

It introduces a model where excitations in fractal media obey a wave-number-dependent parastatistics, linking fractal geometry to fluctuation behavior and noise phenomena.

Findings

The order of parastatistics N(k) scales as k^{D-3} with fractal dimension D.

Density fluctuations are amplified by N(ω) ~ ω^{D-3} in fractal media.

This behavior may explain the origin of 1/f noise in such systems.

Abstract

It is shown that elementary excitations in fractal media obey the so-called parastatistics of a variable order. We show that the order of the parastatistics $N(k) $ is a function of wave numbers $k$ which depends on the fractal dimension $D$ as $N(k) \sim k^{D-3}$ and represents a specific characteristic of such media. This function $N(k)$ defines properties of the ground state for excitations and the behavior of the spectrum of thermal fluctuations. In particular, in fractal media fluctuations of the density acquire an amplification by the factor $N(\omega) \sim \omega ^{D-3}$ which can be related to the origin of $1/f$-noise.