Fractal conductance fluctuations in generic chaotic cavities

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 - beta/2 between 1 and 2. It is governed by the exponent beta (less than or equal to 2) of the power-law distribution P(t)similar to t(-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.