Mainz 2017 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 22: Quantum Gases: Bosons III

Q 22.3: Talk

Tuesday, March 7, 2017, 11:30–11:45, P 204

Quantum Butterfly Effect for Cold Atoms in Optical Lattices: A Trajectory-Based Derivation in Many-Body Space — •Josef Michl, Juan-Diego Urbina, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, Germany

Recently, it was suggested that ⟨[V,Ŵ(t)]^†[V,Ŵ(t)]⟩, is a suitable measure for quantum chaos and the so-called quantum butterfly effect[1], in the sense that the different ordering of the arbitrary operators V and Ŵ with respect to the time evolution operators is sensitive to the hyperbolicity of the underlying classical system. Simple arguments involving Poisson brackets indeed indicate this average to have terms of exponential increase with a rate related to the classical Lyapunov exponent. This behaviour is expected to hold up to time scales of the classical-to-quantum-crossover, known as Ehrenfest or scrambling time. While numerical studies support this claim, analytical explanations are rare and concentrate more on the exponential behaviour and not on the relation between its rate and the Lyapunov exponent. In this presentation we want to fill this gap using semiclassical methods based on the Van-Vleck-propagator for Bose-Hubbard systems, as the picture of interfering classical mean-field trajectories is well suited to provide a quantitative picture in interacting systems. We explicitly discuss the emergence of the Lyapunov exponent and the involved timescales for the simplified picture of the average of the commutator ⟨ [V,Ŵ(t)] ⟩.

[1] J. Maldacena, S. H. Shenker & D. Stanford, J. High Energ. Phys., 2016:106