{getToc} $title={Table of Contents}
Summary
The study examines the relationship between integrability and chaos in the steady state of many-body open quantum systems, using the Lindblad description and level spacing statistics.
Highlights
- The study explores the concept of integrability in open quantum systems.
- The Lindblad description gives rise to two types of integrability.
- Level spacing statistics and the eigenstate thermalization hypothesis (ETH) are used to discriminate between Liouvillian and steady-state chaos.
- The steady-state Hamiltonian H is expanded in the basis of Pauli strings to analyze its structure.
- The operator-size distribution is used to distinguish between chaotic and integrable steady states.
- The study finds that integrable steady states are not "simple" and have contributions from Pauli strings of all possible lengths.
- The results demonstrate that one can effectively use the operator-size distribution to distinguish between chaotic and integrable steady states.
Key Insights
- The study highlights the importance of considering the steady-state sector of the Liouvillian when examining integrability in open quantum systems.
- The use of level spacing statistics and ETH provides a powerful tool for distinguishing between chaotic and integrable steady states.
- The expansion of the steady-state Hamiltonian in the basis of Pauli strings reveals that integrable steady states are not necessarily "simple" and can have complex structures.
- The operator-size distribution provides a useful metric for characterizing the complexity of the steady-state Hamiltonian and distinguishing between chaotic and integrable steady states.
- The study demonstrates that the relationship between integrability and chaos in open quantum systems is more nuanced than in closed systems.
- The results have implications for our understanding of thermalization and the behavior of open quantum systems in the long-time limit.
- The study highlights the need for further research into the properties of steady-state Hamiltonians and the behavior of open quantum systems.
Mindmap
Citation
Richter, J., Sá, L., & Haque, M. (2024). Integrability versus chaos in the steady state of many-body open quantum systems (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.16041