Slow scrambling in sonic black holes

¹ Department of Physics, University of Massachusetts - Amherst, MA 01003, USA
² Departamento de Física, Universidade Federal Rural do Rio de Janeiro - 23897-000 Seropédica, RJ, Brazil
³ Department of Physics and Center for Theory of Quantum Matter, University of Colorado Boulder Boulder, CO 80309, USA
⁴ JILA, NIST and University of Colorado, Department of Physics, University of Colorado Boulder, CO 80309, USA

Received: 27 February 2018
Accepted: 23 April 2018

Abstract

We study from the perspective of quantum information scrambling an acoustic black hole modeled by two semi-infinite, stationary, one-dimensional condensates, connected by a spatial step-like discontinuity, and flowing, respectively, at subsonic and supersonic velocities. We develop a simple analytical treatment based on the Bogoliubov theory of quantum fluctuations which is sufficient to derive an analogue Hawking emission, and we compute out-of-time order correlations (OTOCs) of the Bose density field. We find that a large class of sonic black holes presents slow scrambling contrary to their astrophysical counterparts. This manifests itself in a power law growth of OTOCs in contrast to the exponential increase in time expected for fast scramblers.