1 July 2021 Thu 5 pm

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Understanding the dissipative dynamics of complex quantum systems is of paramount importance to describe quantum matter at large time-scales. A simplified Markovian description, following Lindblad dynamics, is possible whenever characteristic memory times of the environment are much smaller than those of the system. Nonetheless, even in this case, studying the spectral and steady-state properties of Lindblad operators is a daunting task. In this talk, we will first focus on a few examples where dynamics can be obtained exactly [1,2]. We will see that, as in the Hamiltonian case, this procedure is not possible for generic systems. To analyze those, we will follow an approach based on (non- Hermitian) random matrix theory. We will identify the difficulties arising when combining dissipation with quantum chaos, and propose some ways to overcome them [3,4]. In particular, we will discuss our recent proposal of using complex spacing ratios as a signature of dissipative quantum chaos.

[1] Pedro Ribeiro, Tomaž Prosen, Phys. Rev. Lett. 122, 010401 (2019)

[2] J. S. Ferreira and P. Ribeiro, Phys. Rev. B 100, 184422 (2019)

[3] Lucas Sá, Pedro Ribeiro, Tomaž Prosen, J. Phys. A: Math. Theor. 53 305303 (2020)

[4] Lucas Sá, Pedro Ribeiro, Tomaž Prosen, Phys. Rev. X 10, 021019 (2020)

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