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An exactly solvable model for the integrability-chaos transition in rough quantum billiards
Maxim Olshanii1, Kurt Jacobs, Marcos Rigol
1Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA. Maxim.Olchanyi@umb.edu
Nature Communications
|January 26, 2012
Summary
This study introduces a quantum model to understand how quantum systems lose memory of their initial states. The model explains memory loss during the transition from integrability to chaos, crucial for quantum dynamics.
Area of Science:
- Quantum dynamics
- Statistical mechanics
- Quantum chaos
Background:
- Understanding memory loss in quantum systems is a key challenge.
- The integrability-chaos transition is a critical phenomenon in quantum dynamics.
Purpose of the Study:
- To develop a statistically solvable quantum model for memory loss.
- To analyze memory loss across an integrability-chaos transition.
- To provide a theoretical framework for ultracold atom experiments.
Main Methods:
- A simple, statistically solvable quantum model is presented.
- Analysis uses quantum localization-delocalization on the quantum number lattice.
- The model considers a perturbation with no selection rules.
Main Results:
- The model describes memory loss during the integrability-chaos transition.
- It shows a scenario where all quantum number lattice sites couple equally.
- It rigorously justifies relationships observed in ultracold atom systems.
Conclusions:
- The developed quantum model offers insights into quantum memory loss.
- It provides a framework applicable to ultracold atoms and impurity ensembles.
- The model aligns well with numerical simulations.
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