Fractal conductance fluctuations of classical origin

The coherent conductance through mesoscopic structures is well known to show reproducible fluctuations with the variation of an external parameter (e.g. a magnetic field). These fluctuations are caused by interference effects and can be described semiclassically. In systems with mixed (regular and chaotic) classical dynamics {\em fractal} conductance curves are found\footnote{R. Ketzmerick, \textit{Phys. Rev. B} \textbf{54}, 10841 (1996)}. Experiments that study the transition from coherent to incoherent transport showing a change of the fractal dimension with the coherence-length\footnote{A.P. Micolich et al., \textit{Phys. Rev. Lett.} \textbf{87}, 036802 (2001)}, however, seemed to contradict the semiclassical theory of the fractal scaling. We show that there is no contradiction but that the classical dynamics itself already leads to fractal conductance curves\footnote{ H. Hennig, R. Fleischmann, L. Hufnagel and T. Geisel, \textit{Phys. Rev. E} \textbf{76}, 015202 (2007)} explaining the experimental observations. Moreover, we predict fractal classical conductance fluctuations not only in systems with mixed phase space but in purely chaotic systems.