Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 36: Focus: Chaos and Correlation in Quantum Matter (joint session DY/TT)

DY 36.3: Talk

Wednesday, March 14, 2018, 10:15–10:30, EB 107

Out-Of-Time-Ordered Correlators in Chaotic and Critical Many-Body Systems: Path Interference and Scrambling Times — •Josef Rammensee, Benjamin Geiger, Juan Diego Urbina, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, Germany

Out-of-time-ordered correlators ⟨[V,Ŵ(t)]^†[V,Ŵ(t)]⟩ have been identified to be highly suitable tools to identify the onset of chaos in many-body quantum systems[1]. Contrary to already known indicators, the unusual time ordering of the operators is able to directly capture the local hyperbolic nature of the classical counterpart. One expects an exponential increase at short times with a rate related to classical Lyapunov exponents. Numerical studies in chaotic systems[2] indicate a saturation after the time scale for the classical-to-quantum-crossover, known as Ehrenfest or scrambling time. Our numerical studies show, that many-body criticality mimics this behaviour of chaotic systems, however with an exponent given by the local instability rate. We provide insight into the physical origin of the exponential growth and the saturation by using semiclassical methods based on the Van-Vleck-propagator for single- and many-body systems[3]. We show that the notion of interfering classical trajectories is well suited to provide a quantitative picture and we explicitly discuss the emergence of the Lyapunov exponent, resp. instability rates and the relevant time scales.
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T. Engl, J. Dujardin, A. Argüelles et al., PRL 112, 140403 (2014)