Summary
The study explores the relationship between a classical periodic Hamiltonian system and its associated discrete quantum system on a torus in phase space, using the periodically perturbed Harper model. The model exhibits both regular and chaotic behavior, and the study investigates the quantum counterparts of classical chaotic regions.
Highlights
- The periodically perturbed Harper model is used to study the relationship between classical and quantum systems.
- The model exhibits both regular and chaotic behavior in classical systems.
- The study investigates the quantum counterparts of classical chaotic regions.
- The Floquet propagator is used to compute the quasi-energy levels and eigenstates of the quantum system.
- The Husimi distribution is used to visualize the eigenstates in phase space.
- The study finds a close correspondence between the classical and quantum systems, with the quantum system exhibiting similar chaotic behavior.
- The energy dispersion of the unperturbed Hamiltonian is used to estimate the width of the chaotic region.
Key Insights
- The periodically perturbed Harper model provides a useful framework for studying the relationship between classical and quantum systems, particularly in the context of chaotic behavior.
- The Floquet propagator is a powerful tool for computing the quasi-energy levels and eigenstates of the quantum system, allowing for a detailed analysis of the system's behavior.
- The Husimi distribution provides a valuable visualization of the eigenstates in phase space, enabling a direct comparison with the classical system.
- The close correspondence between the classical and quantum systems suggests that the quantum system is able to capture the essential features of the classical chaotic behavior.
- The energy dispersion of the unperturbed Hamiltonian provides a useful estimate of the width of the chaotic region, highlighting the importance of this quantity in understanding the system's behavior.
- The study's findings have implications for our understanding of the relationship between classical and quantum systems, particularly in the context of chaotic behavior.
- The use of the periodically perturbed Harper model and the Floquet propagator provides a useful approach for studying quantum chaos and its relationship to classical chaos.
Mindmap
Citation
Quillen, A. C., & Miakhel, A. S. (2024). Quantum chaos on the separatrix of the periodically perturbed Harper model (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2412.14926