A quantum hydrodynamical description for scrambling and many-body chaos

Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated "quantum hydrodynamics," which is valid at finite $\hbar$ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a "hydrodynamic cloud," and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a "smoking gun" for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.Comment: 48 pages, 9 figures. v2: references added, various clarifications made including an expanded discussion of predictions in the introduction and an expanded discussion of four-point functions, v3: journal versio

Representing Korean Buddhist art and architecture - a 3D animated documentary installation

This practice-led research 'One Mind' - seeks to represent Korean Buddhist architectural aesthetics and Buddhist spiritual ideas using the animated documentary genre as a form of creative representation. It is intended that the piece be shown either as an installation in a gallery, or within a museum or cultural exhibition context. The key goal is to offer this digital artwork to European audiences, in a spirit of engendering the same feeling state as when present in the real monastery, encouraging an understanding of the sacred, and experiencing a form of transcendence. My art work in some ways functions as a digital restoration of sacred architecture outside its real environment and context, and seeks to document cultural heritage and knowledge. One Mind is different from a classic form of documentary, though, because it does not echo the idea of documentary based on live-action footage as a mode of non-fiction record and expression. I have particularly stressed the suggestiveness of the architectural aesthetics and the philosophic principles embedded in the environment. I have sought to bring my own subjective artistic interpretation to Korean Buddhism accordingly, resisting typical character animation and classical narrative, seeking instead, to encourage the viewer to be part of the environment. I focus on the meaning in Buddhist buildings and the landscape they are part of, and dramatise the environment, using the poetic tone of the voice over performance, the sound track of Buddhist chanting, and the visual effects and perspectives of computer generated imagery. This digital visualisation of the Buddhist s spiritual world is informed by a Buddhist s traditional way of life, but, most importantly, by my own past experience, feelings and memory of the Buddhist monastery compound, as a practising artist. My thesis is categorised into eight chapters. Chapter One offers an overview of the aims and objectives of my project. Chapter Two identifies my research questions and my intended methodology. Chapter Three focuses on important background knowledge about Korea s natural and cultural aspects and conditions. Chapter Four offers an analysis of the issue of the Korean cultural identity, suggesting that a more authentic image of Korea and Korean-ness is available in the philosophy and spiritual agenda of Buddhism. Chapter Five addresses the practical ways in which digital restoration of architecture has taken place, identifying three previous cases which both resemble and differ from my own project. Chapter Six looks at the specific characteristics of Korean Seon Buddhism and architecture, and engages with three theoretical approaches about the spatial composition of the monastery, and the ways it may help in constructing the monastery in a digital environment. Chapter Seven offers an evaluation and validation of my artwork, having adopted the approach of creating an animated spiritual documentary to reveal Buddhist philosophy and experience as a model of Korean cultural identity. Chapter Eight offers some conclusions about my intention, process and outcomes