Chaos in Classical D0-Brane Mechanics

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 $N\to \infty$. We show that a classical analog of scrambling occurs with fast scrambling scaling, $t_{\ast }\sim \log S$. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.

Comments: 43 pages, 12 figures. v2: reference added