Particle Motion and Chaos

Abstract

In this note, we explicitly illuminate that the velocity bound in the gravity corresponds to the chaos bound in the quantum system by studying the particle free falling in hyperscaling violating (HV) black brane. We also study the particle falling in a repulsive potential in HV black brane and in the AdS soliton geometry, respectively. We find that the momentum doesn't grow exponentially and chaos is suppressed in the two cases. It is attributed to that when the repulsive potential is introduced or the black hole horizon is absent, the particle is slow down and its trajectory seen by a comoving observer is timelike, which corresponds a weak chaos system. *

Circular Motion of Charged Particles near Charged Black Hole

“…Meanwhile, the study on the near-horizon behavior of the charged particles' static equilibrium pointed out the chaos bound may be violated [20], and in the systems where chaos bound can be violated, the chaos is strengthened [21]. More related calculations have shown the universality of chaos bound in particle motion near black holes, such as the momentum growth of particles' radial falling into black holes [22][23][24][25], the chaos in the null orbits near the horizon [26,27] and the bound of Lyapunov exponent in Kerr-Newman Black Holes [28].…”