1/<i>f</i>noise in random resistor networks: Fractals and percolating systems

Abstract

A general formulation for the spectral noise ${S}_{R}$ of random linear resistor networks of arbitrary topology is given. General calculational methods based on Tellegen's theorem are illustrated for one- and two-probe configurations. For self-similar networks, we show the existence of a new exponent b, member of a whole new hierarchy of exponents characterizing the size dependence of the normalized noise spectrum ${\mathrm{scrS}}_{R}$=${S}_{R}$/${R}^{2}$. is shown to lie between the fractal dimension d\ifmmode\bar\else\textasciimacron\fi{} and the resistance exponent -\ensuremath{\beta}subL. b has been calculated for a large class of fractal structures: Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski gaskets, X lattices, von Koch structures, etc. For percolating systems, scrSsubR is investigated for p&lt;psubc as well as for p&gt;psubc. In particular, an anomalous increase of the noise at p\ensuremath{\rightarrow}psubcsup+ is obtained. A finite-size-scaling function is proposed, and the corresponding exponent b is calculated in mean-field theory.