QM3 Quantum Matter meets Maths   RSS

Lucas Sá 17/06/2020, 11:00 — 12:00 — Online
Lucas Sá, Instituto Superior Técnico and CEFEMA

Random matrix theory of dissipative quantum chaos

Describing complex interacting quantum systems is a daunting task. One very fruitful approach to this problem, developed for unitary dynamics, is to represent the Hamiltonian of a system by a large random matrix. This eventually led to the development of the field of quantum chaos. Arguably, one of its most spectacular achievements was the identification of universal signatures of chaos in quantum systems, characterizing the correlations of their energy levels. In this talk, we will focus on the recent application of (non-Hermitian) random matrix theory to open quantum systems, where dissipation and decoherence coexist with unitary dynamics. First, we will discuss a class of stochastic Lindbladians with random Hamiltonian and independent random dissipation channels (jump operators), as a model for the generator of complicated nonunitary dynamics. We will then explain what difficulties arise when combining dissipation with quantum chaos, and how to overcome them. In particular, we discuss a new non-Hermitian random matrix ensemble with eigenvalues on the torus and how it connects to our recent proposal of using complex spacing ratios as a signature of dissipative quantum chaos.

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Slides of the talk
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The goal of QM3 is to discuss recent topics in quantum matter from a mathematical perspective while building bridges between the physics and mathematics communities.

Organizers: Bruno Mera, João Pimentel Nunes, José Mourão, Pedro Ribeiro, Roger Picken, Vitor Rocha Vieira
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