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DY: Fachverband Dynamik und Statistische Physik
DY 48: Dynamics and Chaos in Many-Body Systems I (joint session DY/TT)
DY 48.3: Talk
Thursday, March 30, 2023, 15:30–15:45, MOL 213
Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems — Felix Meier1, •Mathias Steinhuber2, Juan Diego Urbina2, Daniel Waltner1, and Thomas Guhr1 — 1University of Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany — 2University of Regensburg, Universitätsstr. 31, 93040 Regensburg, Germany
Fast scrambling, quantified by the exponential initial growth of Out-of-Time-Ordered-Correlators
(OTOCs), is the ability to efficiently spread quantum correlations among the degrees of freedom of
interacting systems, and constitutes a characteristic signature of local unstable dynamics. As such,
it may equally manifest both in systems displaying chaos or even in integrable systems around criticality.
We discuss the results from our recent publication [1], where we go beyond these two well-studied regimes with an exhaustive study of the interplay between local
criticality and chaos. We address many-body systems with a well-defined classical (mean-field) limit, as coupled large
spins and Bose-Hubbard chains, thus allowing for semiclassical analysis.
Our aim is to investigate the
dependence of the exponential growth of the OTOCs, defining the quantum Lyapunov exponent λq
on quantities derived from the classical system with mixed phase space, specifically the local stability
exponent of a fixed point λloc as well as the maximal Lyapunov exponent λL of the chaotic region
around it.
[1] Meier, F., Steinhuber, M., Urbina, J. D., Waltner, D. & Guhr, T. arxiv:2211.12147