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DY: Fachverband Dynamik und Statistische Physik

DY 45: Quantum Chaos (joint session DY/TT)

DY 45.6: Vortrag

Freitag, 21. März 2025, 12:45–13:00, H37

The classical Maldacena-Shenker-Standford bound — •Gerrit Caspari, Fabian Haneder, Juan-Diego Urbina, and Klaus Richter — University of Regensburg, Regensburg, Deutschland

The Maldacena-Shenker-Stanford (MSS) bound [1] is a condition on a system's quantum Lyapunov exponent, defined as half the growth rate of the regularised out-of-time-ordered correlator (OTOC), which states that said exponent is bounded by the system's temperature, with, e.g., black holes as characteristic systems saturating the bound.

From the perspective of classical chaos, this is surprising, since the classical Lyapunov exponent seems not to be bounded. We study chaotic quantum systems in a hyperbolic geometry with and without cusps and magnetic fields [2][3] via Selberg's Trace Formula (STF). Through this we derive bounds on the classical Lyapunov exponent from analyticity conditions in the trace formula and relate them to the MSS bound.

We report our progress in studying these bounds using the STF, which entails an investigation of the analyticity condition needed to prove the STF for the partition function of our systems and its relation to possible phase transitions.

[1] Maldacena, J., Shenker, S.H. & Stanford, J. High Energ. Phys. 2016, 106 (2016).

[2] Aurich, R., & Steiner, F. (1992)., Proceedings: Mathematical and Physical Sciences, 437(1901), 693-714

[3] Avron, J.E., Klein, M. & Pnueli, A., Phys. Rev. Lett. 69 (1992)

Keywords: Selberg Trace Fromula; Maldacena bound; Hyperbolic surfaces