Theoretical Physics Seminar: Souvik Banerjee

Title: A universal approach to complexity

Abstract: In this talk, I shall present a general framework in which both the state and the operator complexities can be put on the same footing. This will follow from a generalized definition of complexity based on the violation of the Eigenstate Thermalization Hypothesis. In our formalism, the state complexity is defined in terms of the density matrix of the associated state which, for the operator complexity, lives on a doubled Hilbert space obtained through the channel-state map. I shall discuss how this framework also encompasses nicely, the holographic notions of complexity and explains the universal late-time growth of complexity, followed by saturation. I shall conclude with some open questions.