Fractal Conductance Fluctuations in Generic Chaotic Cavities

TL;DR

This paper demonstrates that conductance fluctuations in chaotic cavities are inherently fractal, with their complexity characterized by a specific fractal dimension related to the system's chaotic dynamics.

Contribution

It introduces the concept that conductance fluctuations in generic chaotic cavities are fractals, linking their fractal dimension to the power law distribution of trajectory durations.

Findings

Conductance vs. parameter graphs are fractals with dimension D=2-b/2.

The fractal nature is governed by the power law exponent b.

Phenomenon observable in semiconductor nanostructures and microwave billiards.

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-b/2 between 1 and 2. It is governed by the exponent b (<2) of the power law distribution P(t) ~ t^{-b} 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.