Floquet Scalar Dynamics in Global AdS

TL;DR

This paper investigates periodically driven scalar fields in global AdS, revealing stable and unstable solutions, black hole formation, and Floquet condensates, with implications for quantum systems and time crystal phenomena.

Contribution

It introduces a new class of Floquet condensates in AdS, maps their stability, and explores quenches and connections to time crystals, extending the understanding of driven holographic systems.

Findings

Identified stable and unstable regions in solution space.

Demonstrated black hole formation for certain perturbations.

Constructed quenches leading to boson stars and Floquet condensates.

Abstract

We study periodically driven scalar fields and the resulting geometries with global AdS asymptotics. These solutions describe the strongly coupled dynamics of dual finite-size quantum systems under a periodic driving which we interpret as Floquet condensates. They span a continuous two-parameter space that extends the linearized solutions on AdS. We map the regions of stability in the solution space. In a significant portion of the unstable subspace, two very different endpoints are reached depending upon the sign of the perturbation. Collapse into a black hole occurs for one sign. For the opposite sign instead one attains a regular solution with periodic modulation. We also construct quenches where the driving frequency and amplitude are continuously varied. Quasistatic quenches can interpolate between pure AdS and sourced solutions with time periodic vev. By suitably choosing the quasistatic path one can obtain boson stars dual to Floquet condensates at zero driving field. We characterize the adiabaticity of the quenching processes. Besides, we speculate on the possible connections of this framework with time crystals.