Fractal Conductance Fluctuations in a Soft-Wall Stadium and a Sinai Billiard

Abstract

Conductance fluctuations have been studied in a soft-wall stadium and a Sinai billiard defined by electrostatic gates on a high mobility semiconductor heterojunction. These reproducible magnetoconductance fluctuations are found to be fractal, confirming recent theoretical predictions of quantum signatures in classically mixed (regular and chaotic) systems. The fractal character of the fluctuations provides direct evidence for a hierarchical phase space structure at the boundary between regular and chaotic motion.