Abstract:

In this talk, I will discuss some general features of operator growth in open quantum systems governed by Lindbladian evolution. I will introduce two orthonormalization techniques, namely Arnoldi and BiLanczos algorithms, using which I will capture the evolution of the operator in an appropriate basis. In these bases, many features of the evolution of operators (including relevant time scales) will emerge naturally. I will motivate these bases choices from results in closed quantum systems. I will utilize the paradigmatic setup of the Sachdev-Ye-Kitaev model to describe the system and environment, and closely related system-environment interaction. I will present numerical results in this setup and derive some analytical results. I will also discuss the nature of correlation function and spectral function in such open quantum systems. Then I will discuss features of a large class of probes (that do not rely on the same choice of basis) in such systems. I will end by mentioning implications of these results in other areas of research, and some open questions/future directions.

References:
[1] Operator dynamics in Lindbladian SYK: a Krylov complexity perspective, JHEP 01 (2024) 094
[2] Operator growth in open quantum systems: lessons from the dissipative SYK, JHEP 03 (2023) 054

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