28 research outputs found
Stability of Charged Global AdS Spacetimes
We study linear and nonlinear stability of asymptotically AdS solutions
in Einstein-Maxwell-scalar theory. After summarizing the set of static
solutions we first examine thermodynamical stability in the grand canonical
ensemble and the phase transitions that occur among them. In the second part of
the paper we focus on nonlinear stability in the microcanonical ensemble by
evolving radial perturbations numerically. We find hints of an instability
corner for vanishingly small perturbations of the same kind as the ones present
in the uncharged case. Collapses are avoided, instead, if the charge and mass
of the perturbations come to close the line of solitons. Finally we examine the
soliton solutions. The linear spectrum of normal modes is not resonant and
instability turns on at extrema of the mass curve. Linear stability extends to
nonlinear stability up to some threshold for the amplitude of the perturbation.
Beyond that, the soliton is destroyed and collapses to a hairy black hole. The
relative width of this stability band scales down with the charge Q, and does
not survive the blow up limit to a planar geometry.Comment: 43 pg, 22 fig. Published version. Appendix adde
Holographic thermalization in finite-size systems
The AdS/CFT correspondence has provided a fascinating window into the real-time dynamics of strongly-coupled QFTs. On the other hand, studies of gravitational collapse in asymptotically global AdS spacetimes have unraveled a surprisingly rich landscape of possible routes to final black hole formation or its absence thereof, that depend both on the precise dynamics and the initial state considered. In the light of the equivalence between gravitational collapse and thermalization implied by the duality, it is natural to wonder which universal lessons these results entail on the out-of-equilibrium physics of isolated, macroscopic quantum systems at strong coupling. This thesis aims to be a modest step in elucidating this question
Convergence of the Fefferman-Graham expansion and complex black hole anatomy
Given a set of sources and one-point function data for a Lorentzian
holographic QFT, does the Fefferman-Graham expansion converge? If it does, what
sets the radius of convergence, and how much of the interior of the spacetime
can be reconstructed using this expansion? As a step towards answering these
questions we consider real analytic CFT data, where in the absence of
logarithms, the radius is set by singularities of the complex metric reached by
analytically continuing the Fefferman-Graham radial coordinate. With the
conformal boundary at the origin of the complex radial plane, real Lorentzian
submanifolds appear as piecewise paths built from radial rays and arcs of
circles centred on the origin. This allows singularities of Fefferman-Graham
metric functions to be identified with gauge-invariant singularities of
maximally extended black hole spacetimes, thereby clarifying the physical cause
of the limited radius of convergence in such cases. We find black holes with
spacelike singularities can give a radius of convergence equal to the horizon
radius, however for black holes with timelike singularities the radius is
smaller. We prove that a finite radius of convergence does not necessarily
follow from the existence of an event horizon, a spacetime singularity, nor
from caustics of the Fefferman-Graham gauge, by providing explicit examples of
spacetimes with an infinite radius of convergence which contain such features.Comment: 29 pages + appendices, 13 figure
Holographic Relaxation of Finite Size Isolated Quantum Systems
We study holographically the out of equilibrium dynamics of a finite size
closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of
a massless scalar field in AdS4. In global coordinates there exists a variety
of evolutions towards final black hole formation which we relate with different
patterns of relaxation in the dual field theory. For large scalar initial data
rapid thermalization is achieved as a priori expected. Interesting phenomena
appear for small enough amplitudes. Such shells do not generate a black hole by
direct collapse, but quite generically an apparent horizon emerges after enough
bounces off the AdS boundary. We relate this bulk evolution with relaxation
processes at strong coupling which delay in reaching an ergodic stage. Besides
the dynamics of bulk fields, we monitor the entanglement entropy, finding that
it oscillates quasi-periodically before final equilibration. The radial
position of the traveling shell is brought into correspondence with the
evolution of the entanglement pattern in the dual field theory. The
entanglement entropy is not only able to portrait the streaming of entangled
excitations, but it is also a useful probe of interaction effects.Comment: 37 pages, 27 figure
Collapse and Revival in Holographic Quenches
We study holographic models related to global quantum quenches in finite size
systems. The holographic set up describes naturally a CFT, which we consider on
a circle and a sphere. The enhanced symmetry of the conformal group on the
circle motivates us to compare the evolution in both cases. Depending on the
initial conditions, the dual geometry exhibits oscillations that we
holographically interpret as revivals of the initial field theory state. On the
sphere, this only happens when the energy density created by the quench is
small compared to the system size. However on the circle considerably larger
energy densities are compatible with revivals. Two different timescales emerge
in this latter case. A collapse time, when the system appears to have dephased,
and the revival time, when after rephasing the initial state is partially
recovered. The ratio of these two times depends upon the initial conditions in
a similar way to what is observed in some experimental setups exhibiting
collapse and revivals
Rigorous bounds on transport from causality
We use causality to derive a number of simple and universal constraints on
dispersion relations, which describe the location of singularities of retarded
two-point functions in relativistic quantum field theories. We prove that all
causal dissipative dispersion relations have a finite radius of convergence. We
then give two-sided bounds on all transport coefficients in units of this
radius, including an upper bound on diffusivity.Comment: 4 pages. New relational bound on sound attenuation, improved test
function, references adde
Holographic quenches with a gap
In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is found provided the width of the oscillating scalar pulse is inversely linked to the energy density communicated by the quench. We propose this to be a general feature of holographic quenches.The work of E.daS. is nanced by the spanish
grant BES-2013-063972. E.L. has been supported by the spanish grant FPA2012-32828 and
SEV-2012-0249 of the Centro de Excelencia Severo Ochoa Programme. The work of J.M.
is supported in part by the spanish grant FPA2011-22594, by Xunta de Galicia (GRC2013-
024), by the Consolider-CPAN (CSD2007-00042), and by FEDER. A.S. is supported by
the European Research Council grant HotLHC ERC-2011-StG-279579 and by Xunta de
Galicia (Conselleria de Educaci on). Part of the numerical calculations were performed at
the Centro de Supercomputaci on de Galicia (CESGA).S
Transseries for causal diffusive systems
The large proper-time behaviour of expanding boost-invariant fluids has
provided many crucial insights into quark-gluon plasma dynamics. Here we
formulate and explore the late-time behaviour of nonequilibrium dynamics at the
level of linearized perturbations of equilibrium, but without any special
symmetry assumptions. We introduce a useful quantitative approximation scheme
in which hydrodynamic modes appear as perturbative contributions while
transients are nonperturbative. In this way, solutions are naturally organized
into transseries as they are in the case of boost-invariant flows. We focus our
attention on the ubiquitous telegrapher's equation, the simplest example of a
causal theory with a hydrodynamic sector. In position space we uncover novel
transient contributions as well as Stokes phenomena which change the structure
of the transseries based on the spacetime region or the choice of initial data.Comment: 23 pages + appendices, 16 figure
Floquet scalar dynamics in global AdS
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.This work of was supported by grants FPA2014-52218-P from Ministerio de Economia
y Competitividad, by Xunta de Galicia ED431C 2017/07, by FEDER and by Grant
Mar a de Maeztu Unit of Excellence MDM-2016-0692. A.S. is happy to acknowledge support
from the International Centre for Theoretical Sciences (ICTS-TIFR), and wants to
express his gratitude to the ICTS community, and especially to the String Theory Group,
for their warm welcome. D.M. thanks the FRont Of pro-Galician Scientists (FROGS) for
unconditional support. A.B. thanks the support of the Spanish program \Ayudas para contratos
predoctorales para la formaci on de doctores 2015" associated to FPA2014-52218-P.
This research has benefited from the use computational resources/services provided by the
Galician Supercomputing Centre (CESGA).S