"Weak Quantum Chaos" and its resistor network modeling

TL;DR

This paper investigates weakly chaotic systems, like nearly integrable optical billiards, showing their Hamiltonian matrices are sparse and textured, and introduces a resistor network model to predict heating rates in cold atom experiments.

Contribution

It introduces a resistor network approach to model weak quantum chaos and predicts heating rates in cold atom optical billiards with vibrating walls.

Findings

Hamiltonian matrices are sparse and textured in weak chaos regimes.

Resistor network modeling relates to semi-linear response and heating rates.

Predicts novel heating rate behavior in cold atom optical billiards.

Abstract

Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with displaceable wall ("piston"). The motion is completely chaotic but with small Lyapunov exponent. The Hamiltonian matrix does not look like one taken from a Gaussian ensemble, but rather it is very sparse and textured. This can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity, respectively. For $g$ we use a resistor network calculation that has a direct relation to the semi-linear response characteristics of the system, hence leading to a novel prediction regarding the rate of heating of cold atoms in optical billiards with vibrating walls.