Which universal features best characterize quantum chaos? Do they hold under dissipative evolution? Can they be translated to the classical realm or are they fundamentally of quantum nature?
We shall first establish a link between the speed of evolution of a quantum state and quantum chaos. While both concepts are known to be bounded independently, no conceptual relationship has yet been looked for, and even less, established. We shall look for a formal relationship and provide the link between these pair of concepts. Second, we aim to shed light on the characterization of dissipative quantum chaos. Through the use of random matrices theory, design of physical models that exhibit chaotic behavior, and numerical simulations, this project will tackle the challenging quantum many-body systems. A systematic study of their statistical properties will help identifying figures of merit to characterize dissipative chaos, and if symmetries in the spectral features generate any universal properties.
This will extend our knowledge and conceptual understanding of the complex quantum many-body systems with chaotic behavior. The knowledge will be delivered in the form of peer-reviewed scientific publications, conference presentations, and organization of one international workshop. The outcomes will include a test-bed model suited for experimental implementation in current technological platforms. Impact is long-term and aims at bridging the communities of open quantum systems and quantum chaos.