Floquet scalar dynamics in global AdS

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.

Gravitational wave driving of a gapped holographic system

“…This is in line with previous observations for nonlinear normal modes of massless scalar fields in global AdS[32], boson stars[17], and solitonic solutions in Einstein-Maxwell-scalar theory[35].…”

“…Decoherence is 5 This argument can also be applied to a massless real scalar field in global AdS 4 . In this case, the normal mode frequencies are given by Ω n = 3 + 2n, and the Fourier modes of TPSs are restricted to odd multiples of ω, so we expect the strongest resonance at ω = Ω 0 /3 = 1, which is outside the region studied in [17] (see Fig.33 in this reference). dual to the formation of a black hole, whose horizon z h covers the tip of the cigar, z h < z 0 .…”

“…Fig.10 shows an example only of the latter situation. If the transition between the two kinds of TMSs we have found is to be interpreted as a type I critical phenomenon, the following relation must hold [17]…”

“…We will refer to these geometries as time-periodic solutions (TPSs). The numerical procedure needed to construct them follows the methods developed for a scalar field in global AdS [17] [31] [32] [33]. The strategy starts by first elucidating, through a perturbative analysis, the expected content of Fourier harmonics of a TPS.…”

“…The spectrum {λ n (ω), n ∈ N} of perturbations is obtained by solving the linear system subjected to the mentioned Dirichlet boundary conditions. This is performed through the same pseudospectral method used to find the TPSs themselves (see appendix D in [17] for details). Solutions always come in pairs (±λ n ,b (1) ,P (1) , ±b (2) , ±P (2) ).…”