Chaos in Classical D0-Brane Mechanics

TL;DR

This paper investigates chaos in the classical limit of D0-brane matrix mechanics, calculating Lyapunov exponents and confirming properties like fast scrambling and k-locality, with implications for understanding quantum chaos.

Contribution

It provides the first detailed calculation of Lyapunov spectra in classical D0-brane dynamics and confirms the fast scrambling behavior predicted by holographic principles.

Findings

Largest Lyapunov exponent determined precisely

Lyapunov spectrum approaches a smooth limit as N increases

Classical analog of fast scrambling confirmed

Abstract

We study chaos in the classical limit of the matrix quantum mechanical system describing D0-brane dynamics. We determine a precise value of the largest Lyapunov exponent, and, with less precision, calculate the entire spectrum of Lyapunov exponents. We verify that these approach a smooth limit as $N \rightarrow \infty$. We show that a classical analog of scrambling occurs with fast scrambling scaling, $t_* \sim \log S$. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.