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.
*TX is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. AC02-05CH11231 within the Ultrafast Materials Science Program (KC2203). TS acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), in particular the Discovery Grant [RGPIN-2020-05842], the Accelerator Supplement [RGPAS-2020-00060], and the Discovery Launch Supplement [DGECR-2020-00222]. XC acknowledges support from the DOE grant DESC0019380, and from Gordon and Betty Moore Foundation’s EPIC initiative, Grant GBMF4545.
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Presenters
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Tianrui Xu
- Physics, University of California, Berkeley