Stability of Branched Flow from a Quantum Point Contact

In classically chaotic systems, small differences in initial conditions are exponentially magnified overtime. However, it was observed experimentally that the (necessarily quantum) ‘‘branched flow’’ pattern ofelectron flux from a quantum point contact (QPC) traveling over a random background potential in two-dimensional electron gases remains substantially invariant to large changes in initial conditions. Sincesuch a potential is classically chaotic and unstable to changes in initial conditions, it was conjectured thatthe origin of the observed stability is purely quantum mechanical, with no classical analog. In this Letter,we show that the observed stability is a result of the physics of the quantum point contact and the nature ofthe experiment. We show that the same stability can indeed be reproduced classically, or quantummechanically. In addition, we explore the stability of the branched flow with regards to changes in theeigenmodes of the quantum point contact.