Chaotic instability in the BFSS matrix model

TL;DR

This paper investigates chaotic instability in the BFSS matrix model, revealing fractal structures and singular behaviors that explain membrane instability and relate to supermembrane quantum dynamics.

Contribution

It introduces a simplified dynamical system to analyze chaotic instability in the BFSS model and identifies fractal structures and singular behaviors associated with membrane instability.

Findings

Fractal structure in the chaotic scattering process.

Singular behavior of the time delay function.

Chaotic instability as a fundamental membrane instability mechanism.

Abstract

Chaotic scattering is a manifestation of transient chaos realized by the scattering with non-integrable potential. When the initial position is taken in the potential, a particle initially exhibits chaotic motion, but escapes outside after a certain period of time. The time to stay inside the potential can be seen as lifetime and this escape process may be regarded as a kind of instability. The process of this type exists in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model in which the potential has flat directions. We discuss this chaotic instability by reducing the system with an ansatz to a simple dynamical system and present the associated fractal structure. We also show the singular behavior of the time delay function and compute the fractal dimension. This chaotic instability is the basic mechanism by which membranes are unstable, which is also common to supermembranes at quantum level.