Abstract
We review recent developments encompassing the description of quantum chaos in holography. We discuss the characterization of quantum chaos based on the late time vanishing of out-of-time-order correlators and explain how this is realized in the dual gravitational description. We also review the connections of chaos with the spreading of quantum entanglement and diffusion phenomena.
Highlights
The characterization of quantum chaos is fairly complicated
Possible approaches range from semiclassical methods to random matrix theory: in the first case one studies the semiclassical limit of a system whose classical dynamics is chaotic; in the later approach the characterization of quantum chaos is made by comparing the spectrum of energies of the system in question to the spectrum of random matrices [1]
New insights into quantum chaos have come from black holes physics! In the context of so-called gaugegravity duality [2,3,4], black holes in asymptotically AdS spaces are dual to strongly coupled many-body quantum systems
Summary
The characterization of quantum chaos is fairly complicated. Possible approaches range from semiclassical methods to random matrix theory: in the first case one studies the semiclassical limit of a system whose classical dynamics is chaotic; in the later approach the characterization of quantum chaos is made by comparing the spectrum of energies of the system in question to the spectrum of random matrices [1]. (Another interesting perspective on the characterization of chaos in the context of (regularized) AdS2/CFT1 is provided by [17,18,19].) due the lack of the author’s expertise, we did not cover the recent developments in the direct field theory calculations of OTOCs. We focus on the case of d−dimensional gravitational systems with d ⩾ 3, which excludes the case of gravity in AdS2 and SYK-like models [13,14,15,16]. This includes calculations for CFTs [20], weakly coupled systems [21, 22], random unitary models [23,24,25], and spin chains [26,27,28,29,30]
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