Exploring integrability-chaos transition with a sequence of independent perturbations

TL;DR

This paper investigates how adding independent perturbations to a system transitions it from integrability to chaos, demonstrating that the number of involved eigenstates increases linearly with scatterers, with observable experimental implications.

Contribution

It introduces a general rule for how independent perturbations enhance chaos and provides criteria for when this increase occurs, supported by numerical simulations.

Findings

NPC increases linearly with scatterers

Decay of observable fluctuation variance observed

Eigenstate thermalization approached in experiments

Abstract

A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by the number of principal components (NPC) -- the number of integrable system eigenstates involved into the non-integrable one, which increases linearly with the number of strong scatterers. This rule is a particular case of the general effect of an additional perturbation on the system chaotic properties. The perturbation independence criteria supposing the system chaoticity increase are derived here as well. The effect can be observed in experiments with photons or cold atoms as the decay of observable fluctuation variance, which is inversely proportional to NPC, and, therefore, to the number of scatterers. This decay indicates that the eigenstate thermalization is approached. The results are confirmed by numerical calculations for a harmonic waveguide with zero-range scatterers along its axis.