Erlangen 2018 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 10: Quantum Gases (Bosons) I

Q 10.6: Vortrag

Montag, 5. März 2018, 11:45–12:00, K 2.020

Quantum Chaos of Cold Atoms in Optical Lattices: A Trajectory-Based Analysis of Out-Of-Time-Ordered Correlators in Many-Body Space — •Josef Rammensee, Juan Diego Urbina, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, Germany

To address the question of how to measure many-body quantum chaos, i.e. the influence of classical chaos underlying a quantum many-particle system, so-called out-of-time-ordered correlators ⟨[V,Ŵ(t)]^†[V,Ŵ(t)]⟩ have been identified to be highly suitable tools[1]. Contrary to already known indicators, their unusual time ordering of the operators is able to directly capture the hyperbolic nature of the classical counterpart, as one expects an exponential increase at short times with a rate related to classical Lyapunov exponents. Arguments based on a naive quantum-classical correspondence motivate this expectation. Numerical studies further indicate, without quantitative explanation, a later saturation after the time scale for the classical-to-quantum-crossover, known as Ehrenfest or scrambling time. Here 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 Bose-Hubbard systems[2]. We show that the notion of interfering classical mean-field trajectories is well suited to provide a quantitative picture for interacting bosonic systems. We explicitly discuss the emergence of the Lyapunov exponent and the relevant time scales.
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