GQFI-WST Seminar: Arjun Kar "A hierarchy of complexity growth from integrability and chaos"
Quantum complexity has been conjectured to be relevant for black hole interiors. In particular, Susskind has conjectured a generic form of complexity growth and saturation for maximally chaotic systems like black holes. In this tak, Arjun Kar (UBC) studies the complexity of time evolution in free, integrable, and chaotic systems with N degrees of freedom using geodesic complexity techniques. He demonstrates that the growth rate of this complexity is related to more familiar properties of physical theories like 1) the existence of creation/annihilation operators and 2) smeared thermal two-point functions. Using these properties, he finds that the complexity saturates in free, integrable, and chaotic theories at time scales which are on the order of N^{1/2}, polynomial in N, and exponential in N, respectively. This results in the free theory improve an existing bound in the complexity theory literature, and the results in chaotic theories are based only on coarse properties of the spectrum and eigenstates.
The Virtual Seminar Series “GQFI-Warsaw String Theory” (GQFI-WST) is a joint initiative between the strings/holography groups at the Albert Einstein Institute (AEI) in Potsdam and the University Warsaw. The calendar for upcoming GQFI-WST seminars can be found here: https://gqfi.aei.mpg.de/node/3.
This talk is primarily based on arXiv:2101.02209 [hep-th] (https://arxiv.org/abs/2101.02209) and arXiv:1905.05765 [hep-th] (https://arxiv.org/abs/1905.05765).
This talk was recorded on April 21st, 2021 at the Albert Einstein Institute in Potsdam-Golm.