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Does scrambling equal chaos?
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Focusing on semiclassical systems, we show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.
Forward citations
Cited by 2 Pith papers
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Higher-Order Corrections to Scrambling Dynamics in Brownian Spin SYK Models
Operator growth in Brownian spin SYK is solved beyond leading order with a generating-function 1/N perturbation theory; higher-order corrections set the late-time universal (two-body) and parity-protected (three-body)...
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Quasinormal modes and complexity in saddle-dominated SU(N) spin systems
A family of SU(2) and SU(3) Lipkin-Meshkov-Glick-type Hamiltonians reproduces de Sitter quasinormal-mode densities of states, and late-time probes reveal integrability beneath saddle-dominated scrambling.
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