Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Dynamics in many-body systems: Equilibration and localization I (joint session DY/TT)

DY 6.3: Talk

Monday, April 1, 2019, 10:30–10:45, H19

Out-Of-Time-Ordered Correlators in critical systems - Instability and the onset of chaos — •Dominik Hahn, Benjamin Geiger, Quirin Hummel, and Klaus Richter — Universität Regensburg

It is known from mean field theory that a system of bosons with attractive contact interaction in one dimension exhibits a quantum phase transition at a certain critical coupling. This transition has its manifestation in the formation of a local instability in the integrable mean-field dynamics. By adding an external potential, we investigate the transition from integrability to chaos in this system. A characteristic feature of chaotic motion, the exponential sensitivity to initial conditions, can be also detected in the corresponding quantum mechanical system using Out-Of-Time-Ordered Correlators (OTOCs). It can be shown, that a local instability is sufficient to generate an exponential growth of certain OTOCs. After breaking the integrability, we find evidence, that the OTOC growth is affected by an additional exponent, which can be related to the largest Lyapunov exponent of the system.