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A quantum hydrodynamical description for scrambling and many-body chaos · Around

2017

A quantum hydrodynamical description for scrambling and many-body chaos

Blake, Mike, Lee, Hyunseok, Liu, Hong

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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.

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