Black holes and the butterfly effect

Black holes and the butterfly effect

21 Apr 2014 | Stephen H. Shenker and Douglas Stanford
This paper explores the relationship between entanglement and scrambling in strongly coupled field theories using holography. The authors study how small perturbations to a thermofield double state can disrupt correlations between two subsystems, L and R, in a holographic setup. They show that adding a small number of quanta to one side of the system, released a scrambling time in the past, destroys local two-sided correlations. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. The authors also discuss string- and Planck-scale corrections to this setup and its relevance to the firewall controversy. The paper begins by introducing the concept of entanglement and its role in quantum systems. It then discusses the thermofield double state and its holographic realization in the AdS/CFT correspondence. The authors analyze how perturbations to this state can disrupt entanglement and lead to scrambling, a chaotic behavior where initially similar states evolve to be quite different. They show that scrambling can disrupt certain kinds of entanglement, and this interplay is at the heart of the firewall proposal. The authors use a qubit model to illustrate the effect of scrambling on entanglement. They then describe a holographic model, using the BTZ black hole geometry, to study the loss of local correlation between the L and R sides. They calculate the mutual information between regions A and B in the two CFTs and show how it is affected by the perturbation. They also discuss the effect of the shock wave on geodesic distances and correlation functions. The paper concludes by discussing the implications of these results for black hole physics, including the connection to the firewall controversy. The authors show that the time it takes for a system to scramble and become thermal is conjectured to be $ t \sim \beta \log S $, where S is the entropy of the system. They also discuss the effects of string- and Planck-scale corrections to the results and the importance of the logarithmic behavior in black hole physics. The authors emphasize the importance of the fast scrambling time and its connection to the logarithmic dependence on entropy. They also discuss the implications of their results for the firewall proposal and the connection between entanglement and scrambling in black hole physics.This paper explores the relationship between entanglement and scrambling in strongly coupled field theories using holography. The authors study how small perturbations to a thermofield double state can disrupt correlations between two subsystems, L and R, in a holographic setup. They show that adding a small number of quanta to one side of the system, released a scrambling time in the past, destroys local two-sided correlations. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. The authors also discuss string- and Planck-scale corrections to this setup and its relevance to the firewall controversy. The paper begins by introducing the concept of entanglement and its role in quantum systems. It then discusses the thermofield double state and its holographic realization in the AdS/CFT correspondence. The authors analyze how perturbations to this state can disrupt entanglement and lead to scrambling, a chaotic behavior where initially similar states evolve to be quite different. They show that scrambling can disrupt certain kinds of entanglement, and this interplay is at the heart of the firewall proposal. The authors use a qubit model to illustrate the effect of scrambling on entanglement. They then describe a holographic model, using the BTZ black hole geometry, to study the loss of local correlation between the L and R sides. They calculate the mutual information between regions A and B in the two CFTs and show how it is affected by the perturbation. They also discuss the effect of the shock wave on geodesic distances and correlation functions. The paper concludes by discussing the implications of these results for black hole physics, including the connection to the firewall controversy. The authors show that the time it takes for a system to scramble and become thermal is conjectured to be $ t \sim \beta \log S $, where S is the entropy of the system. They also discuss the effects of string- and Planck-scale corrections to the results and the importance of the logarithmic behavior in black hole physics. The authors emphasize the importance of the fast scrambling time and its connection to the logarithmic dependence on entropy. They also discuss the implications of their results for the firewall proposal and the connection between entanglement and scrambling in black hole physics.
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