SKM 2021 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 7: Focus Session: Facets of Many-Body Quantum Chaos (organised by Markus Heyl and Klaus Richter) (joint session DY/TT)
DY 7.2: Vortrag
Mittwoch, 29. September 2021, 10:15–10:30, H6
Exploring the bound on chaos due to quantum criticality — •Mathias Steinhuber, Juan-Diego Urbina, and Klaus Richter — University of Regensburg, Regensburg, Germany
The ‘bound on chaos’ proposed by Maldacena, Shenker and Stanford [1] predicts a temperature-dependent upper bound on the initial exponential growth rate λOTOC≤ 2π T for out-of-time-order correlators (OTOCs) in quantum systems with chaotic classical limit. We explore the temperature dependence of the quantum Lyapunov exponent λOTOC in Bose-Hubbard systems near criticality of the ground state [2]. We find the conditions for a non-trivial temperature dependence satisfying the bound, indicating the requirement that the system shows signatures of classical instability at the ground state while reaching the semiclassical regime at the same time. This is guaranteed by many-body systems with a well defined mean-field limit close to a bifurcation [3].
- ] Maldacena J., Shenker S. H. & Stanford D. A bound on chaos. Journal of High Energy Physics 2016, 106 (2016).
- ] Hummel, Q., Geiger, B., Urbina, J. D. & Richter, K. Reversible Quantum Information Spreading in Many-Body Systems near Criticality. Phys. Rev. Let. 123, 160401 (2019).
- ] Eilbeck, J., Lomdahl, P. & Scott, A. The discrete self-trapping equation. Physica D: Nonlinear Phenomena 16, 318-338 (1985).