Complexity, chaos and the moving D3-brane

TL;DR

This paper investigates the quantum circuit complexity of fluctuations around a moving D3-brane in AdS5×S5, revealing that non-BPS states tend to evolve into chaos more readily than BPS states, with implications for holographic thermodynamics.

Contribution

It applies quantum information methods to analyze the complexity evolution of D3-brane fluctuations, linking chaos emergence to BPS and non-BPS states in holography.

Findings

Non-BPS branes exhibit chaotic complexity evolution at late times.

BPS branes show less tendency towards chaos in their complexity dynamics.

Implications for understanding thermalization and chaos in holographic systems.

Abstract

We use the wave-function method developed in area of quantum information to investigate the quantum circuit complexity of the small quantum fluctuations around the probe $D_3$ brane moving in $AdS_5\times S^5$ bulk. In our consideration, the reference and target states are chosen as the vacuum state and the squeezed quantum state respectively. The evolution of parameters characterizing the squeezed quantum state are governed by the time-dependent $Schr\ddot{o}dinger$ equation, in which the Hamiltonian operator is derived from the perturbative action of $D_3$ brane. For a quantum chaotic system, some recent works indicate that the evolution of quantum circuit complexity could provide equivalent information like the out-of-time-order correlators. Basing on this inference, our results show that the quantum fluctuations around the non-BPS brane manifestly evolve into the chaotic regime at the late time, while the chaotic behavior is not easy to observe in case of BPS brane. In holographic viewpoint, it implies that the thermodynamic system consist of the $N=4$ supersymmetric particles in non-BPS states evolve into a chaotic system more easily than the one in BPS state.