Piecewise Interference and Stability of Branched Flow

TL;DR

This paper reveals that quantum branched flow exhibits surprising stability against large perturbations due to piecewise interference, challenging classical chaos expectations and introducing the concept of piecewise classical stable paths.

Contribution

It introduces the concept of piecewise classical stable paths (PCSPs) to explain quantum stability in chaotic systems, extending traditional scattering theory.

Findings

Quantum branched flow remains stable under large perturbations.

Piecewise interference explains the stability of quantum trajectories.

The theory applies to various physical systems, including nanostructures and ocean waves.

Abstract

The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are largely ignored by the quantum dynamics. The origin of this stability is accounted for by the piecewise nature of the interference, which is largely ignored by the traditional theory of scattering. Incorporating it into our theory, we introduce the notion of piecewise classical stable paths(PCSPs). Our theory shall have implications for many different systems, from electron transport in nanostructures, light propagation in nonhomogeneous photonic structures to freak wave formations in oceans.