Examining instabilities due to driven scalars in AdS

Cownden, Brad

doi:10.1007/jhep12(2020)013

Cited by 4 publications

(5 citation statements)

References 44 publications

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“…The long-time fate afterwards is difficult to foresee as the numerical simulations lose convergence before any conclusive result is reached. It would be interesting to prove this effect more explicitly, maybe along the lines pursued in [18].…”

Section: Jhep11(2023)230mentioning

confidence: 98%

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Resonant drivings in global AdS

Mas,

Mayo

2023

J. High Energ. Phys.

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We revisit the case of a real scalar field in global AdS4 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., 〈ϕ〉 = 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.

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Section: Jhep11(2023)230mentioning

confidence: 98%

“…From the bulk perspective, the exchange of energy-momentum through the boundary acts by blocking the turbulent cascade. It would be interesting to clarify this issue by resorting to a resonant analysis of the non-normalisable solutions, probably along the lines of [18].…”

Section: Jhep11(2023)230mentioning

confidence: 99%

Resonant drivings in global AdS

Mas,

Mayo

2023

J. High Energ. Phys.

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“…It is also possible to consider the injection of a scalar field pulse at the conformal boundary, similar to the Vaidya solution, which corresponds to allowing non-normalizable modes of the scalar field. 2 This scenario is less well-understood than the case of an initial scalar profile, but see [35][36][37]. Due to computational requirements discussed below, we will consider the complexity in black hole formation with nontrivial initial conditions rather than nontrivial boundary conditions for the scalar field.…”

Section: Jhep12(2021)135mentioning

confidence: 99%

Complexity of scalar collapse in anti-de Sitter spacetime

Frey

Grehan

Srivastava

2021

J. High Energ. Phys.

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We calculate the volume and action forms of holographic complexity for the gravitational collapse of scalar field matter in asymptotically anti-de Sitter spacetime, using numerical methods to reproduce the geometry responding to the oscillating field over multiple crossing times. Like the scalar field pulse, the volume complexity oscillates quasiperiodically before horizon formation. It also shows a scaling symmetry with the amplitude of the scalar field. The action complexity is also quasiperiodic with spikes of increasing amplitude.

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“…The Hamiltonian (1.1) may appear not-too-familiar to many readers, but, as a matter of fact, the corresponding classical Hamiltonian system frequently arises as a controlled approximation to weakly nonlinear partial differential equations (PDEs) in strongly resonant domains, originating from a number of branches of physics and mathematics. Specifically, classical systems corresponding to (1.1), together with some closely related variations, have been studied in the following contexts: gravitational dynamics in anti-de Sitter (AdS) spacetimes [44][45][46][47][48][49][50][51] (typically, motivated by the AdS instability conjecture [52,53]); related dynamical problems for classical relativistic fields [54][55][56][57][58][59][60]; nonrelativistic nonlinear Schrödinger equations describing, among other things, the dynamics of Bose-Einstein condensates in harmonic potentials [61][62][63][64][65][66][67][68][69][70]; and integrable models for turbulence [71][72][73][74][75][76][77]. These classical systems display, for different choices of C nmkl , a wide range of analytic and dynamical patterns ranging from full solvability [71][72][73][74] to Lax-integrability [71]…”

Section: Introductionmentioning

confidence: 99%

Bounds on quantum evolution complexity via lattice cryptography

et al. 2022

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We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate 'complexity metric' must be used that takes into account the relative difficulty of performing 'nonlocal’ operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to \sim 10^4∼104.

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Examining instabilities due to driven scalars in AdS

Cited by 4 publications

References 44 publications

Resonant drivings in global AdS

Resonant drivings in global AdS

Complexity of scalar collapse in anti-de Sitter spacetime

Bounds on quantum evolution complexity via lattice cryptography

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