Weak quantum chaos
Kukuljan, Ivan (Author), Grozdanov, Sašo (Author), Prosen, Tomaž (Author)

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Out-of-time-ordered correlation functions (OTOCs) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local operators are bounded, an OTOC of local observables is bounded as well and thus its exponential growth is merely transient. As a better measure of quantum chaos in such systems, we propose, and study, the density of the OTOC of extensive sums of local observables, which can exhibit indefinite growth in the thermodynamic limit. We demonstrate this for the kicked quantum Ising model by using large-scale numerical results and an analytic solution in the integrable regime. In a generic case, we observe the growth of the OTOC density to be linear in time. We prove that this density in general, locally interacting, nonintegrable quantum spin and fermionic dynamical systems exhibits growth that is at most polynomial in time—a phenomenon, which we term weak quantum chaos. In the special case of the model being integrable and the observables under consideration quadratic, the OTOC density saturates to a plateau.

Keywords:quantum mechanics, quantum chaos
Tipology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publisher:American Physical Society
Number of pages:str. 060301-1-060301-6
Numbering:Vol. 96, iss. 6
ISSN on article:2469-9950
DOI:10.1103/PhysRevB.96.060301 Link is opened in a new window
COBISS.SI-ID:3179364 Link is opened in a new window
Copyright:American Physical Society
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Record is a part of a journal

Title:Physical review
Publisher:American Physical Society
COBISS.SI-ID:2997348 This link opens in a new window

Document is financed by a project

Funder:EC - European Commission
Funding Programme:H2020
Project no.:694544
Name:Open many-body non-equilibrium systems

Secondary language

Keywords:kvantna mehanika, teorija kaosa

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