Regensburg 2022 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 4: Many-Body Quantum Dynamics 1 (joint session DY/TT)

TT 4.5: Talk

Monday, September 5, 2022, 11:00–11:15, H20

Transition from localized to uniform scrambling in locally hyperbolic systems — •Mathias Steinhuber, Juan-Diego Urbina, and Klaus Richter — University of Regensburg, Regensburg, Germany

A major signature of Quantum Chaos is the fast scrambling of quantum correlations, quantified by the exponential initial (pre-Ehrenfest time) growth of out-of-time-order correlators (OTOCs) and by their later saturation. As previously shown by [1] and [2], there is a significant difference in the short time dynamics of the OTOCs in integrable systems around hyperbolic fixed points depending on the initial state being localized or uniform (high-temperature). In these cases, the exponential regime is given respectively by twice the instability-exponent 2λ or only once the stability-exponent λ of the hyperbolic fixed point. We show that a local wave-packet can have a clear dynamical transition between these two reported exponential-regions within the pre-Ehrenfest-time regime. Thus, the question arises on how to decide, based on the properties of the hyperbolic fixed point which of the two scenarios applies in each particular situation.

1. Hummel, Q., Geiger, B., Urbina, J. D. & Richter, K. Reversible Quantum Information Spreading in Many-Body Systems near Criticality. Phys. Rev. Lett. 123, 160401 (2019).
2. Xu, T., Scaffidi, T. & Cao, X. Does Scrambling Equal Chaos? Phys. Rev. Lett. 124, 140602 (2020).