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FRI: Friday Contributed Sessions

FRI 3: Quantum Chaos

FRI 3.2: Talk

Friday, September 12, 2025, 11:00–11:15, ZHG003

High dimensional hyperbolic motion is maximally quantum chaotic — •Gerrit Caspari, Fabian Haneder, Juan Diego Urbina, and Klaus Richter — University of Regensburg

The Maldacena-Shenker-Stanford (MSS) bound is a condition on a system's quantum Lyanpunov exponent, defined as the growth rate of the regularized out-of-time-order correlator (OTOC) with respect to a thermal state. It states that the exponent is bounded by the system's temperature T, with maximally chaotic quantum systems, e.g. black holes, being defined by its saturation. Thus, it is expected that non-gravitational, maximally chaotic systems should have a gravitational dual.

In this contribution, we study the OTOC of a particle on a hyperbolic surface in arbitrary dimensions. Using the Wigner-Moyal formalism and a saddle-point approximation based on exact results for the mean level density given by the Selberg trace formula we show compliance to the MSS bound for low temperatures and finite dimensions and the asymptotic approach to a saturation formally obtained for infinite dimensions. To this end, a controlled asymptotic analysis of the interplay between dimensionality, temperature and quantum corrections is mandatory and nicely displays a transition from a sqrt(T) behavior into a T behavior of the quantum Lyapunov exponent. Together with the previous analysis of previous works, our results strongly indicate that high-dimensional hyperbolic motion admits an effective description in terms of emergent gravitational degrees of freedom.

Keywords: Quantum Chaos; Quantum Gravity; Selberg Trace Formula; Maldacena-Shenker-Stanford bound