Random matrix theory of open quantum systems and dissipative quantum chaos

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• Lucas Sá (Universidade de Lisboa)
• Friday 03 February 2023, 11:15-12:15
• TCM Seminar Room.

If you have a question about this talk, please contact Jan Behrends.

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Describing interacting quantum systems in the presence of dissipation is a daunting task. One very fruitful approach to this problem, developed for unitary dynamics, is to represent the Hamiltonian of a generic system by a large random matrix. This approach eventually led to the development of the field of quantum chaos. Here, I will give an overview of the recent application of (non-Hermitian) random matrix theory to open quantum systems, where dissipation and decoherence coexist with unitary dynamics. First, I will discuss the relaxation timescales and steady states of three representative examples of increasing physical relevance: random Lindbladians, open free fermions, and dissipative strongly-interacting SYK models. Second, I will argue that complex spacing ratios are a powerful signature of dissipative quantum chaos, illustrating it with the case of boundary-driven spin-chain Lindbladians. Finally, I will present a recent systematic symmetry classification of many-body Lindblad superoperators.

This talk is part of the Theory of Condensed Matter series.

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