Dynamical transition; Ehrenfest; Exponential growth; Fixed points; Hyperbolic system; Localised; Quantum correlations; Time ordering; Time-scales; Unstable dynamics; Statistical and Nonlinear Physics; Statistics and Probability; Condensed Matter Physics; Quantum Physics; Physics - Other; Nonlinear Sciences - Exactly Solvable and Integrable Systems
Abstract :
[en] Fast scrambling of quantum correlations, reflected by the exponential growth of out-of-time-order correlators (OTOCs) on short pre-Ehrenfest time scales, is commonly considered as a major quantum signature of unstable dynamics in quantum systems with a classical limit. In two recent works [Phys. Rev. Lett. 123, 160401 (2019)0031-900710.1103/PhysRevLett.123.160401] and [Phys. Rev. Lett. 124, 140602 (2020)10.1103/PhysRevLett.124.140602], a significant difference in the scrambling rate of integrable (many-body) systems was observed, depending on the initial state being semiclassically localized around unstable fixed points or fully delocalized (infinite temperature). Specifically, the quantum Lyapunov exponent λ_{q} quantifying the OTOC growth is given, respectively, by λ_{q}=2λ_{s} or λ_{q}=λ_{s} in terms of the stability exponent λ_{s} of the hyperbolic fixed point. Here we show that a wave packet, initially localized around this fixed point, features a distinct dynamical transition between these two regions. We present an analytical semiclassical approach providing a physical picture of this phenomenon, and support our findings by extensive numerical simulations in the whole parameter range of locally unstable dynamics of a Bose-Hubbard dimer. Our results suggest that the existence of this crossover is a hallmark of unstable separatrix dynamics in integrable systems, thus opening the possibility to distinguish the latter, on the basis of this particular observable, from genuine chaotic dynamics generally featuring uniform exponential growth of the OTOC.
Disciplines :
Physics
Author, co-author :
Steinhuber, Mathias ; Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
Schlagheck, Peter ; Université de Liège - ULiège > Département de physique > Physique quantique statistique
Urbina, Juan Diego ; Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
Richter, Klaus ; Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
Language :
English
Title :
Dynamical transition from localized to uniform scrambling in locally hyperbolic systems.
DFG - Deutsche Forschungsgemeinschaft Studienstiftung des Deutschen Volkes
Funding text :
We are grateful for financial support from the Deutsche Forschungsgemeinschaft (German Research Foundation) through Project Ri681/15-1 (Project No. 456449460) within the Reinhart Koselleck Programme. M.S. further acknowledges funding through the Studienstiftung des Deutschen Volkes.
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