Resonant Drivings in Global AdS

TL;DR

This paper investigates the dynamics of a scalar field in global AdS$_4$ under periodic and stochastic driving, revealing conditions for stable solutions, resonant behaviors, and collapse phenomena.

Contribution

It introduces a detailed analysis of resonant and non-resonant driving protocols, including adiabatic deformations, quasi-periodic solutions, and stochastic noise effects in AdS.

Findings

Periodic solutions with vanishing v.e.v. are identified.

Driving near normal mode frequencies can lead to black hole formation or stable states.

Stochastic driving shows a phase transition from stability to collapse.

Abstract

We revisit the case of a real scalar field in global AdS$_4$ subject to a periodic driving. We address the issue of adiabatic preparation and deformation of a time-periodic solution dual to a Floquet condensate. Then we carefully study the case of driving close to the normal mode resonant frequencies. We examine different slow protocols that adiabatically change the amplitude and/or the frequency of the driving. Traversing a normal mode frequency has very different results depending upon the sense of the frequency modulation. Generally, in the growing sense, the geometry reaches a periodically-modulated state, whereas in the opposite one, it collapses into a black hole. We study the suppression points. These are periodic solutions that are dual to a scalar field with vanishing $v.e.v., \langle \phi\rangle = 0$, instead of vanishing source. We also investigate quasi-periodic solutions that are prepared by driving with a combination of two normal resonant frequencies. We observe that, while the driving is on, the non-linear cascading towards higher frequencies is strongly suppressed. However, once the driving is switched off, the cascading takes over again, and in some cases, it eventually brings the solution to a collapse. Finally, we study the driving by a non-coherent thermal ensemble of resonant drivings that model stochastic noise. Our numerical results suggest the existence of stable regular solutions at sufficiently low temperature and a transition to collapse above some threshold.