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Related Experiment Video

Updated: May 30, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

"Weak quantum chaos" and its resistor network modeling.

Alexander Stotland¹, Louis M Pecora, Doron Cohen

¹Department of Physics, Ben-Gurion University of the Negev, IL-84 105 Beer-Sheva, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 30, 2011

Summary

This summary is machine-generated.

Random matrix theory fails for weakly chaotic systems. We studied cold atoms in optical billiards, finding sparse Hamiltonian matrices characterized by parameters s and g, predicting energy absorption rates.

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Area of Science:

Quantum chaos
Atomic physics
Statistical mechanics

Background:

Standard random matrix theory (RMT) is insufficient for weakly chaotic or interacting systems.
Optical billiards with cold atoms offer a tunable platform to study quantum dynamics.

Purpose of the Study:

To investigate the behavior of cold atoms in a nearly integrable optical billiard with a displaceable wall.
To characterize the Hamiltonian matrix of such systems beyond standard RMT.
To predict the energy absorption rate of cold atoms in optical billiards with vibrating walls.

Main Methods:

Analysis of cold atom dynamics in a nearly integrable optical billiard.
Characterization of the Hamiltonian matrix using parameters 's' (percentage of large elements) and 'g' (connectivity).
Application of resistor network calculations to determine 'g' and its relation to semilinear response.

Main Results:

The Hamiltonian matrix for this system is sparse and textured, deviating from Gaussian ensembles.
Parameters 's' and 'g' effectively describe the matrix properties.
Resistor network calculations provide insights into semilinear response characteristics.

Conclusions:

A new model is proposed for weakly chaotic systems where standard RMT fails.
The study predicts the energy absorption rate for cold atoms in optical billiards with vibrating walls.
The findings have implications for understanding energy transfer in complex quantum systems.