Chaos in classical D0-brane mechanics

Abstract

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 → ∞. We show that a classical analog of scrambling occurs with fast scrambling scaling, t ∗ ∼ log S. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.