Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 42: Focus: Many-Body Quantum Chaos

DY 42.3: Talk

Thursday, April 4, 2019, 10:30–10:45, H20

Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators — •Josef Rammensee, 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 found 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 as one expects an exponential increase at short times with a rate related to classical Lyapunov exponents. Numerical studies in chaotic systems[2] further indicate a saturation after the time scale for the classical-to-quantum-crossover, known as Ehrenfest or scrambling time. 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[4] 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, and the relevant time scales.
Maldacena, Shenker, and Stanford, JHEP 2016:106 (2016)
Rozenbaum, Ganeshan, Galitski, PRL 118, 086801 (2017)
Engl, Dujardin, Argüelles, Schlagheck, Richter, J. D. Urbina, PRL 112, 140403 (2014)
Rammensee, Urbina, Richter, PRL 121, 124101 (2018)