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

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.