Fractal conductance fluctuations in generic chaotic cavities

Abstract

It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of conductance vs externally changed parameter, e.g., magnetic field, is a fractal with dimension D=2-\ensuremath{\beta}/2 between 1 and 2. It is governed by the exponent \ensuremath{\beta} (\ensuremath{\leqslant}2) of the power-law distribution P(t)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$ for a classically chaotic trajectory to stay in the cavity up to time t, which is typical for chaotic systems with a mixed (chaotic and regular) phase space. The phenomenon should be observable in semiconductor nanostructures and microwave billiards. \textcopyright{} 1996 The American Physical Society.