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A Physical Measure for Characterizing Crossover from Integrable to Chaotic Quantum Systems.

Chenguang Y Lyu¹, Wen-Ge Wang^1,2

¹Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.

Entropy (Basel, Switzerland)

|February 25, 2023

Summary

Researchers developed a new measure to characterize the transition from integrable to chaotic quantum systems. This quantity reveals three distinct regimes within the transition region, aiding in understanding quantum dynamics.

Keywords:

Lipkin-Meshkov-Glick (LMG) model eigenstate statistics integrability-chaos cross-over quantum chaos transition probability

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Area of Science:

Quantum mechanics
Statistical physics

Background:

Characterizing the transition from quantum integrability to chaos is a fundamental challenge.
Existing measures often lack the sensitivity to precisely define intermediate regimes.

Purpose of the Study:

To introduce and validate a novel quantity for measuring the crossover from integrable to chaotic quantum systems.
To analyze the integrability-chaos transition in the Lipkin-Meshkov-Glick model using this new measure.

Main Methods:

Studying a quantity describing the response of system eigenstates to small perturbations.
Computing this quantity from the distribution of rescaled components of perturbed eigenfunctions.
Performing numerical simulations on the Lipkin-Meshkov-Glick model.

Main Results:

The proposed measure effectively quantifies the transition from integrability to chaos.
Numerical simulations clearly delineate three subregions within the transition: nearly integrable, crossover, and nearly chaotic.
The measure provides a physical interpretation related to the prohibition of level transitions.

Conclusions:

The developed measure offers a robust tool for analyzing quantum integrability-chaos transitions.
The Lipkin-Meshkov-Glick model exhibits a rich transition landscape with distinct dynamical regimes.
This work advances the understanding of quantum system dynamics and phase transitions.