Chaotic instability in the BFSS matrix model

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.

Gauge Field Theory Vacuum and Cosmological Inflation

“…The Yang-Mills energy momentum tensor T µν in ( 13), (15) [75,76,77,79] and therefore opens a room of possibilities for a vector field driven cosmology and inflation [3]. The space homogeneous gauge fields are described by a classical mechanical system, so called Yang-Mills classical mechanics (YMCM) [75,76,77,79,78,80,81,82,84,85,86,87,88,89,90,91,92,93,95,96,97,98,99], it represents the bosonic part of the matrix models [85,86,81,87,88,89,90,91] and were considered in the context of the cosmological models in [109,110,111,112,113,114,115,116,117,118,…”

“…These scales lead to a much shorter universe live-time, but, importantly, to finite non-diverging time intervals 7 . In the case of Type II solution to be considered in the next section, when 0 ≤ γ 2 < γ 2 c and ã(0) ≥ µ 2 , the deceleration parameter q is negative and the scale factor grows exponentially with the inflation of a finite duration (97 ) that undergoes a continuous transition to a linear in time growth (99).…”

“…and at t t s (b 2 → ∞) the vacuum density tends to zero Ω vac → 0 meaning that the influence of the gauge field theory vacuum on the evolution of the universe fades out turning into a linear expansion (99).…”