Does scrambling equal chaos?
ORAL
Abstract
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.
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Presenters
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Tianrui Xu
Physics, University of California, Berkeley
Authors
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Tianrui Xu
Physics, University of California, Berkeley
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Thomas Scaffidi
Physics, University of Toronto
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Xiangyu Cao
Ecole Normale Supérieure, Paris, Physics, Ecole Normale Supérieure (Paris)